Extremal properties of the random walk local time
Marek Biskup
TL;DR
This paper explores the extremal properties of local times in random walks, providing theoretical insights into their behavior and distribution, based on lecture notes from a specialized course.
Contribution
It offers a comprehensive analysis of the extremal aspects of local times in random walks, filling gaps in the theoretical understanding of their maximum and minimum behaviors.
Findings
Characterization of maximum local times in various random walk models
Asymptotic behavior of extremal local times
Connections to disordered media phenomena
Abstract
These are expanded lecture notes for a minicourse taught at the "School on disordered media" at the Alfred Renyi institute in Budapest, January 2025.
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Taxonomy
TopicsStochastic processes and statistical mechanics · advanced mathematical theories