Maximum of Dyson Brownian motion and non-colliding systems with a boundary
Alexei Borodin, Patrik L. Ferrari, Michael Praehofer, Tomohiro, Sasamoto, Jon Warren
TL;DR
This paper establishes a probabilistic equivalence between the maximum of GUE Dyson's Brownian motion and non-colliding systems with a boundary, extending classical reflection results.
Contribution
It generalizes the relation between Brownian motion maxima and reflected Brownian motion to Dyson's Brownian motion with boundary conditions.
Findings
Proves an equality-in-law between the maximum of Dyson's Brownian motion and non-colliding systems with a wall.
Extends classical reflection principles to complex interacting particle systems.
Provides a new probabilistic link in random matrix theory and stochastic processes.
Abstract
We prove an equality-in-law relating the maximum of GUE Dyson's Brownian motion and the non-colliding systems with a wall. This generalizes the well known relation between the maximum of a Brownian motion and a reflected Brownian motion.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and statistical mechanics · Point processes and geometric inequalities