• Book of abstracts
  • Plenary Lecture or Open Public Lecture
    • Transport in Disordered Media
    • On the norm of random matrices with a tensor structure
    • On rates in the central limit theorem for a class of convex costs
    • Superdiffusive Central Limit Theorem for the critical Stochastic Burgers Equation
    • The cutoff phenomenon for Markov chains
    • What AI will not tell you about white noise
    • Exchangeability in Continuum Random Trees
    • On estimating Fréchet means
    • Minimal surfaces in a random environment:
    • On the derivation of mean-curvature flow and its fluctuations from microscopic interactions
    • Critical long-range percolation
    • Bootstrap percolation and kinetically constrained models: universality results
  • IS01: Statistics for Stochastic Processes
    • Fractional interacting particle system: drift parameter estimation via Malliavin calculus
  • IS02: Heavy-Tailed Phenomena in Networks
    • Emergence of heavy-tailed cascades in flow networks through a unified stochastic overload framework.
  • IS03: Self-Organized Criticality
    • The particle density in mean-field Activated Random Walk and the 2D sandpile
    • The density conjecture for activated random walk
    • Self-organized criticality and avalanches in 2D forest fires
  • IS04: Geometry of Random Walks
    • Three-dimensional loop-erased random walks
  • IS05: Random Planar Geometry
    • Percolation of Gaussian free field and loop soup in dimension two
    • Schramm-Loewner evolution contains a topological Sierpi'nski carpet when \(\kappa\) is close to 8
  • IS06: Lévy-Type Processes
    • Liouville theorems for Fourier Multipliers
  • IS07: Inhomogeneous Spatial Graph Models
    • High-intensity Voronoi percolation on manifolds
    • Annulus crossing probabilities in geometric inhomogeneous random graphs
  • IS08: Emerging Topics in Stochastic Finance
    • Convergence Analysis of Real-time Recurrent Learning (RTRL) for a class of Recurrent Neural Networks
    • Stochastic filtering equations for diffusions on infinite graphs
    • Median process in fragmented crypto-markets: robust estimation, hedging
  • IS09: Random Partitions
  • IS10: Martingales and Their Applications in PDEs and Harmonic Analysis
    • Plurisuperharmonic functions and sharp inequalities for analytic BMO functions and martingales
    • Gaussian coupling on the Wiener space and stochastic differential equations
  • IS11: Long Range Percolation Models
    • Hausdorff dimension of the critical clusters for the metric graph Gaussian free field
  • IS12: Superlinear Stochastic Partial Differential Equations
    • Stochastic reaction diffusion equations with superlinear coefficients
  • IS13: Recent Developments in Branching Structures
    • Sharp LlogL condition for supercritical Galton-Watson processes with countable types
  • IS14: Probabilistic Aspects of Data Privacy
  • IS15: Extremes of Gaussian and Related Random Fields
  • IS16: Stochastic Stability
    • Poisson Hail on a Wireless Ground
    • Stability analysis of two-class retrial systems with constant retrial rates and general service times
    • The random timestep Euler method and its continuous dynamics
  • IS17: Applications of Stochastic Analysis to Deep Learning
    • The Proportional Scaling Limit of Neural Networks
  • IS18: SDEs: Analysis, Approximation, Inference
    • Feynman-Kac formula for the gradient of the Dirichlet problem and its applications
    • Statistical inference for locally stable regression
    • A Tail-Respecting Explicit Numerical Scheme for Lévy-Driven SDEs With Superlinear Drifts
    • The Feynman-Kac formula for the gradient of the Dirichlet problem and its applications
  • IS19: Branching and Interacting Particle Systems
    • Discounted tree sums in branching random walks
    • Explosion of Crump-Mode-Jagers processes with critical immediate offspring
  • IS20: Non-Equilibrium Statistical Mechanics
    • Stochastic and dynamical approaches to non-Hermitian matrix-valued processes
    • Collisions of the supercritical Keller-Segel particle system
    • Assistant Professor
  • IS21: On Nodal Random Variables
  • IS22: Probabilistic Foundations of Machine Learning
  • IS23: Inference in Stochastic Networks
    • Inference in infinite-server queueing networks with Poisson sampling
    • Inference in dynamic random graphs
  • IS24: Random Media and Limit Theorems
    • Random Motzkin paths with KPZ related asymptotics
    • Random walk approximation for the stationary distribution of the open ASEP
  • IS25: Quasi-Stationary Distributions and Applications
  • IS26: Invariant Measures and Scaling Limits of Integrable Systems
    • Simple nonlinear PDEs inspired by billiards
  • IS27: Rough Analysis
    • New algebraic structures in rough analysis and their applications
    • Strong regularization of differential equations with integrable drifts by fractional noise
  • IS28: Random Matrices and Combinatorial Structures
    • The spectrum of dense kernel-based random graphs
  • IS29: Probabilistic and Statistical Study of Systems of Interacting Neurons
    • Asymptotic behaviour of networks of Hopfield-like neurons
    • Nonparametric estimation of the jump rate in mean field interacting systems of neurons
  • IS30: Mixing Times for Random Walks
    • Mixing of a random walk on a randomly twisted hypercube
    • Random walk on the small-world network model in 3 or more dimensions
  • IS31: Random Growth and KPZ Universality
    • Two-layer Gibbs line ensembles
    • On the global solutions of the KPZ fixed point
    • Scaling limit of half-space KPZ equation
    • KPZ equation from some interacting particle systems
  • IS32: Stochastic Eco-Evolutionary Models
    • Convergence of a general structured individual-based model with possibly unbounded growth, birth and death rates
  • CS01: Advanced Bayesian Methods and Statistical Innovations in High-Dimensional Mixed-Type Data Analysis and Neuroimaging
    • Bayesian Sparse Kronecker Product Decomposition for Multi-task Mixed-effects Regression with Tensor Predictors
    • Low-rank regularization of Fréchet regression models for distribution function response
  • CS02: Recent Progress on Stein’s Method
    • Brownian approximation for deterministic dynamical systems: a Stein’s method approach
    • Normal approximation for exponential random graphs
    • High-dimensional bootstrap and asymptotic expansion
  • CS03: Renormalization in Probability and Quantum Field Theory
  • CS04: Branching Processes as Models for Structured Populations
  • CS05: Recent Advances in Interacting Brownian Particle Systems and Their Mean-Field Limits
    • Convex order and increasing convex order for McKean-Vlasov processes with common noise
  • CS06: Control and Estimation in Stochastic Systems
    • Goggin’s corrected Kalman Filter: Guarantees and Filtering Regimes
    • Sequential policies and the distribution of their total rewards in dynamic and stochastic knapsack problems
    • Optimal Sparse Graph Design for Stochastic Matching
  • CS07: Stochastic Properties of Time-Dependent Random Fields
    • Limit theorems for spatiotemporal functionals of Gaussian fields
    • Statistical inference for cylindrical processes on the sphere
  • CS08: New Frontiers in Stochastic Quantisation
  • CS09: Limit Theorems Through the Lens of Wiener Chaos and Stein-Malliavin Techniques
  • CS10: Dynamics of Stochastic Particle Systems
    • Collisions in one-dimensional particle systems
    • Heat kernel bounds for Keller-Segel type finite particles
    • Optimal Bounds For The Dunkl Kernel In The Dihedral Case
  • CS11: Spectrally negative Lévy models with level-dependent features
    • Optimality of a barrier strategy in a spectrally negative Lévy model with a level-dependent intensity of bankruptcy
    • Lévy processes under level-dependent Poissonian switching
    • Fluctuations of Omega-Killed Level-Dependent Spectrally Negative Levy Processes
  • CS12: Recent Advances in Non-Markovian Processes and Random Fields
    • Fourier dimension of the graph of fractional Brownian motion with H>1/2
    • Scaling limit of dependent random walks
    • Sample path properties of Gaussian random fields with slowly varying increments
  • CS13: Complex Systems I
    • Langevin equation in quenched heterogeneous landscapes
  • CS14: Complex Systems II
    • The role of the fractional material derivative in Lévy walks
  • CS15: Complex Systems III
  • CS16: Recent Advances in Financial and Actuarial Mathematics
    • Dr
    • Valuation of multi-region CoCoCat bonds
    • Expectiles in probabilistic forecasting of electricity prices with risk management implications
    • Implicit control for L'evy-type dividend-impulse problem
  • CS17: Dependent Percolation Models: Discrete and Continuum
    • Percolation in lattice k-neighbor graphs
  • CS18: Recent Advances in Generalised Preferential Attachment Models
    • Persistence of hubs in preferential attachment trees with vertex death.
  • CS19: Reinforcement Models: Elephant Random Walk
    • Step Reinforced Random Walks with Regularly Varying Memory
    • Some results for variations of the Elephant random walk
    • Elephant Random Walk with multiple extractions
  • CS20: Parameter Randomization Methods for Stochastic Processes
    • Anomalous diffusive processes with random parameters. Theory and Applications.
    • Lévy processes with values in the cone of non-negatively defined matrices
    • Multiple scaled multivariate distributions and processes
  • CS21: Stochastic Numerics on Manifolds
    • Fundamental theorem for mean square convergence of SDEs on Riemannian manifolds
    • Kinetic Langevin equations on Lie groups with a geometric mechanics approach
  • CS22: Noncommutative Stochastic Processes
    • Stochastic optimization in free probability
    • Affine fixed-point equations in free probability
    • What can Lévy processes tell us about compact quantum groups?
  • CS23: Stochastic Processes Under Constraints
    • Persistence of Strongly Correlated Stationary Gaussian fields: From Universal Probability Decay to Entropic Repulsion
    • Partially-homogeneous reflected random walk on the quadrant
    • Brownian Motion Subject to Time-Inhomogeneous Additive Penalizations
  • CS24: Recent Advances in Statistical Inference for Nonstationary Stochastic Processes
    • Spectral analysis of harmonizable processes with spectral mass concentrated on lines
    • Statistical Properties of Oscillatory Processes with Stochastic Modulation in Amplitude and Time
    • Deep learning-based estimation of time-dependent parameters in the AR(1) model
  • CS25: Volterra Gaussian Processes
    • Self-intersection local times of Volterra Gaussian processes in stochastic flows
    • Volterra Gaussian Processes as the fluctuations of the total quasi-steady-state-approximation of Michaelis–Menten enzyme kinetics
    • Strong solutions for singular SDEs driven by long-range dependent fractional Brownian motion and other Volterra processes
  • CS26: Inference for Stochastic Equations
    • Parameter estimation for SDEs with Rosenblatt noise
    • Statistical inference for semi-linear SPDEs using spatial information
  • CS27: Global and Non-Global Solutions of Semilinear Fractional Differential Equations
    • On the explosion time of a semilinear stochastic partial differential equations driven by a mixture of Brownian and fractional Brownian motion
    • Global and Non-global Solutions of a Fractional Reaction-Diffusion Equation Perturbed by a Fractional Noise
    • Explosion in finite time of solutions of a time-fractional semilinear heat equation
  • CS28: Propagation of Chaos in Life Science Models
    • Strong propagation of chaos for systems of interacting particles with nearly stable jumps
  • CS29: Computing the Invariant Distribution of Linear and Non-Linear Diffusions by Ergodic Simulation
    • Approximation of the invariant distribution for a class of ergodic jump diffusions
    • Computing the invariant distribution of McKean-Vlasov SDEs by ergodic simulation with rates in Wasserstein distance.
  • CS30: Gaussian Processes for Fractional Dynamics and Limiting Behaviour
    • On some fractional stochastic models based on Mittag-Leffler integrals
    • Fractional rough diffusion Bessel processes: reflection, asymptotic behavior and parameter estimation
    • Finite-velocity random motions governed by a modified Euler-Poisson-Darboux equation
  • CS31: Extremes, Sojourns and Related Functionals of Gaussian Processes
    • On a Weak Convergence Theorem for the Normalized Maximum of Stationary Gaussian Processes with a Trend
  • CS32: Advances in Statistical Inference for Spatial Point Processes
    • Conformal Novelty Detection for Replicate Point Patterns
    • Minimax Estimation of the Structure Factor of Spatial Point Processes
  • CS33: LLMs and ML in Dynamic Risk Control
    • LLM-Driven Stock Movement Prediction
  • CS34: Non-Local Operators in Probability: Anomalous Transport, Stochastic Resettings and Diffusions with Memory
    • Non-Local Boudary Value Problems and Stochastic Resettings
  • CS35: Edge and Spectrum of Heterogeneous Ensembles
  • CS36: Probabilistic Graphical Models
  • CS37: Recent progresses on McKean-Vlasov equations and mean field interacting particle systems
    • Strong solution and Large deviation principles for the Multi-valued McKean-Vlasov SDEs with jumps
    • Recent results on mean field interacting particle systems and McKean-Vlasov equations
  • CS38: Random Geometric Systems
    • Ordering and convergence of large degrees in random hyperbolic graphs
    • Large-Deviation Analysis for Canonical Gibbs Measures
  • CS39: Recent Advances in Stochastic Differential Equations
    • Regularity of the density of singular SDEs driven by fractional noise and application to McKean-Vlasov equations
    • Supercritical SDEs driven by fractional Brownian motion with divergence free drifts
  • CS40: Dynamical Systems Modelling
    • Multiple Stopping Porosinski’s Problem
    • Quantitative Bounds for Kernel based Q-learning in continuous spaces
    • Multiple Stopping Problems and Their Applications
    • On the stopping problem of Markov chain and Odds-theorem
  • CS41: Asymptotic Behavior of Selected Markov Random Dynamical Systems
    • Law of the iterated logarithm for Markov semigroups with exponential mixing property in the Wasserstein distance
    • Hybrid stochastic particle model of proliferating cells with chemotaxis.
    • Limit theorems for a general class of Markov processes on Polish spaces: with applications to PDMPs with random flow switching.
  • CS42: Recent Advances in Random Walks and Random Polymers in Random Environments
    • Central Limit Theorem for 2d directed polymers
  • CS43: Volatility by Diffusion: A Novel Approach to SABR
    • Characterization of the Probability Distribution in the SABR Model
    • Measuring volatility: deterministic and stochastic perspectives (regularization by noise)
    • Characterization of moments in the SABR model
  • CS44: Stable-Type Processes
    • On mean exit time from a ball for symmetric stable processes
    • On ``dynamic’’ approximation scheme for L'evy processes
    • Nodal sets of supersolutions to Schrödinger equations based on symmetric jump processes
  • CS45: Lévy processes and random walks in random and deterministic environments and their spectral theory
  • CS46: Asymptotic behaviors for McKean-Vlasov Stochastic Differential Equations
    • Averaging principles and central limit theorems for multiscale McKean-Vlasov stochastic systems
    • Asymptotic behaviors for Volterra type McKean-Vlasov integral equations with small noise
  • CS47: Dynamical Systems Modelling II
  • CS48: Path Integral Formalism for Stochastic Processes: Applications in Physics and Biology
    • Multiplicative Noise and Entropy Production Rate in Stochastic Processes With Threshold
  • CS49: Analysis of Singular Diffusions and Related Areas
    • A bridge between Random Matrix Theory and Schramm-Loewner Evolutions Theory
    • A bridge between Random Matrix Theory and Schramm-Loewner Evolutions Theory
    • Asymptotic behavior of the Brownian motion with singular drifts
  • CS50: Advances in Operator Algebras and Free Probability

SPA 2025

CS49: Analysis of Singular Diffusions and Related Areas

Organizer: Adina Oprisan (New Mexico State University)

A bridge between Random Matrix Theory and Schramm-Loewner Evolutions Theory

Vlad Margarint

I will describe a new method that connects two areas of Probability Theory: Schramm-Loewner Evolutions (SLE) and Random Matrix Theory. This machinery opens new avenues of research that allow the use of modern techniques from one field to another. One aspect of this research direction is centered in an interacting particle systems model, namely the Dyson Brownian motion. In the first part of the talk, I will introduce basic ideas of SLE theory, then I will describe the connection with modern techniques from Random Matrix Theory via a first application of our method. I will finish the talk with some open problems that emerge using this newly introduced toolbox. This is a joint work with A. Campbell and K. Luh.

Bibliography

\([1]\) Campbell, A., Luh, K., Margarint, V. (2025). Rate of Convergence in Multiple SLE using Random Matrix Theory. Random Matrices Theory and Applications.

A bridge between Random Matrix Theory and Schramm-Loewner Evolutions Theory

Vlad Margarint

I will describe a new method that connects two areas of Probability Theory: Schramm-Loewner Evolutions (SLE) and Random Matrix Theory. This machinery opens new avenues of research that allow the use of modern techniques from one field to another. One aspect of this research direction is centered in an interacting particle systems model, namely the Dyson Brownian motion. In the first part of the talk, I will introduce basic ideas of SLE theory, then I will describe the connection with modern techniques from Random Matrix Theory via a first application of our method. I will finish the talk with some open problems that emerge using this newly introduced toolbox. More details available at margarintvlad.com. This is a joint work with A. Campbell and K. Luh.

Bibliography

\([1]\) Campbell, A., Luh, K., Margarint, V. (2025). Rate of Convergence in Multiple SLE using Random Matrix Theory. Random Matrices Theory and Applications.

Asymptotic behavior of the Brownian motion with singular drifts

Adina Oprisan

We discuss the influence of a power law drift on the exit time of the Brownian motion from the half line when the order of the drift at 0 and infinity is different. We find that the first hitting time of 0 is finite almost surely, even when the drift near 0 is positive and unbounded, and study the asymptotic behavior of the process at the time of hitting. We find that the behavior of the process near the origin does not influence the time to hit 0 over long time periods and derive subexponential estimates for the tail distribution of the hitting time. Our results extend to the case in which the drifts are regularly varying functions at 0 respectively infinity. This talk is based on a joint work with Dante DeBlassie and Robert Smits.