Explicit formulae in probability and in statistical physics

TL;DR

This paper explores Marc Yor's influential work on planar Brownian motion windings and exponential functionals of Levy processes, highlighting explicit calculation techniques relevant to statistical physics and disordered systems.

Contribution

It provides a detailed analysis of Yor's results and methods, emphasizing explicit formulae and their applications in polymers and disordered systems.

Findings

Explicit formulae for windings of planar Brownian motion

Connections between exponential functionals of Levy processes and disordered systems

Techniques enabling precise calculations in statistical physics

Abstract

We consider two aspects of Marc Yor's work that have had an impact in statistical physics: firstly, his results on the windings of planar Brownian motion and their implications for the study of polymers; secondly, his theory of exponential functionals of Levy processes and its connections with disordered systems. Particular emphasis is placed on techniques leading to explicit calculations.