Andrew Wade (Durham University) – Perimeter length of the convex hull of hyperbolic Brownian motion
- Date
- @ MALL, 14:00
- Location
- MALL
- Speaker
- Andrew Wade
- Affiliation
- Durham University
- Short bio [AI generated]
- Professor Andrew Wade is a Professor of Probability in the Department of Mathematical Sciences at Durham University. His research focuses on probability theory and stochastic processes, particularly random walks, random spatial graphs, interacting particle systems, and probabilistic models motivated by physics and other applications. Professor Wade completed his PhD in Mathematical Sciences at Durham and, after positions at the Universities of Bath, Bristol, and Strathclyde, returned to Durham in 2012, where he is now a leading member of its probability research group. He is a Fellow of the Higher Education Academy and an active collaborator in the Probability in the North East research network. His work has made significant contributions to the theory of random walks, reflected stochastic processes, convex hulls of random paths, and related areas of applied probability, with publications in leading journals such as The Annals of Probability and Probability Theory and Related Fields.
- Category
- Probability
In this talk, I will relate the expected hyperbolic length of the perimeter of the convex hull of the trajectory of Brownian motion in the hyperbolic plane to an expectation of a certain exponential functional of a one-dimensional real-valued Brownian motion, and hence derive small- and large-time asymptotics for the expected hyperbolic perimeter. In contrast to the case of Euclidean Brownian motion with non-zero drift, the large-time asymptotics are a factor of two greater than the lower bound implied by the fact that the convex hull includes the hyperbolic line segment from the origin to the endpoint of the hyperbolic Brownian motion. This is joint work with Chinmoy Bhattacharjee (Hamburg) and Rik Versendaal (Delft).