Vysotskiy - The Isoperimetric Problem for Convex Hulls and the Large Deviations Rate Functions
Explores large deviations principle for convex hull areas in planar random walks, analyzing optimal trajectories and solving the Euler-Lagrange equation for various rate functions.
Minkowski Content of the Scaling Limit of 3D Loop-Erased Random Walk
Explores Minkowski content of 3D loop-erased random walk's scaling limit, focusing on discrete space analysis, one-point function estimates, and ball-hitting probabilities in Z^3.
Limit Shapes of Non-Intersecting Brownian Bridges via Harmonic Envelope
Explores limit shapes of non-intersecting Brownian bridges, focusing on macroscopic patterns and connections to random Young tableaux using the tangent plane method and harmonic envelope.
Scaling Limit of Colored Asymmetric Simple Exclusion Process
Explore the scaling limit of colored ASEP using Yang-Baxter equation and Gibbs line ensemble techniques, revealing connections to the KPZ universality class and related probabilistic objects.
Randomness in Dynamical Systems - Lecture 1
Explore randomness in dynamical systems, focusing on its role and implications in geophysical fluid dynamics and climate modeling. Learn about stochastic aspects and their impact on system behavior.
Modelling the Erosion of Epigenetic Landscapes in Cancer and Ageing
Explore mathematical models of epigenetic landscapes in cancer and aging, focusing on erosion processes and their implications for disease progression and cellular behavior.
Constrained Stochastic Processes: From Brownian Motion to Run-and-Tumble Particles
Explore constrained stochastic processes, including Brownian motion, Lévy flights, and run-and-tumble particles. Learn effective dynamics for generating constrained trajectories in various scenarios.
Resolution of a Hundred Year Old Problem on Lattice Random Walks and Its Application to Study Inelastic Collisions
Explore a century-old lattice random walk problem and its implications for inefficient diffusion in complex systems.
Generation of Stochastic Trajectories - Applications to Complex Systems
Explore stochastic trajectory generation and its applications in complex systems, focusing on interdisciplinary physics concepts and advanced modeling techniques.
Numerical Methods for Quasi-Stationary Distributions
Explore numerical techniques for calculating quasi-stationary distributions in complex systems, enhancing understanding of long-term behavior in stochastic processes.
Dynamical Spectral Transition for Optimization in Very High Dimensions
Explore dynamical spectral transitions in high-dimensional optimization, examining mathematical concepts and their applications in complex systems and data analysis.
Applications of Duality - Lecture 3
Explore applications of dual processes in Markov chains, including strong stationary times, eigenvalue interpretation, and solutions to the Peres conjecture for Birth and Death chains.
Duality and Intertwining in Markov Chains - Lecture 2
Explore advanced Markov chain analysis through embedded processes, intertwining relations, and various dualities. Gain insights into stationarity and extensions to set and measure-valued duals.
Optimal Transport and High-Dimensional Probability - Langevin Dynamics via Calculus
Explore optimal transport, high-dimensional probability, and Langevin dynamics through advanced calculus techniques in this mathematical deep dive.
Graph Limit for Interacting Particle Systems on Weighted Deterministic and Random Graphs
Explore graph limits for interacting particle systems on weighted deterministic and random structures in this advanced mathematical lecture.
Numerical Methods for SDEs with Singular Coefficients - Lecture 3
Explore numerical methods for SDEs with singular coefficients in this advanced mathematics lecture by Benjamin Jourdain, focusing on cutting-edge techniques and applications.
Numerical Methods for SDEs with Singular Coefficients - Lecture 1
Explore numerical methods for stochastic differential equations with singular coefficients in this advanced mathematics lecture by Benjamin Jourdain.
Numerical Methods for SDEs with Singular Coefficients - Lecture 2
Explore numerical methods for SDEs with singular coefficients in this advanced mathematics lecture by Benjamin Jourdain, focusing on cutting-edge techniques and applications.
Steady States and Dynamics of the Aggregation-Diffusion Equation - Lecture 2
Explore steady states and dynamics of aggregation-diffusion equations in this advanced mathematics lecture by Yao Yao, part of a thematic meeting on interacting particle systems.
Steady States and Dynamics of the Aggregation-Diffusion Equation - Lecture 1
Explore steady states and dynamics of the aggregation-diffusion equation in this advanced mathematics lecture by Yao Yao at CIRM's thematic meeting on interacting particle systems.
Gradient Flows for Sampling and Their Deterministic Interacting Particle Systems
Explore gradient flows for sampling and deterministic interacting particle systems in this mathematical conference talk by Dejan Slepčev.