ISSBG2025 0 CALIN

Описание: OVIDIU CALIN
Exploring Brownian Motion on Diverse Structures

In this talk, we delve into the captivating interplay between stochastic processes and geometric structures, with a focus on Brownian motion as it unfolds across lines, circles, curves, and planar domains. We investigate the intricate probability laws governing these motions and reveal surprising phenomena that arise when randomness meets geometry.

A highlight of the presentation is the study of the so-called Brownian triangle—a triangle whose vertices are determined by three independent planar Brownian motions. We analyze the distribution of its area, uncovering remarkable stochastic properties and connections to classical geometric probability. In addition, the talk addresses the relationship between curvature and randomness. We explore how the curvature of a curve influences the behavior of a Brownian particle traveling near it over small time intervals, shedding new light on the interplay between deterministic geometry and probabilistic dynamics.
Attendees will gain insight into modern techniques in stochastic geometry and see how these methods open doors to novel applications and theoretical advancements in the understanding of complex random systems.

Department of Mathematics and Statistics, Eastern Michigan University, USA