Mean square displacement of Brownian paths perturbed by bounded pair potentials
Volker Betz, Tobias Schmidt, Mark Sellke
TL;DR
This paper investigates how bounded pair potentials influence the mean square displacement of Brownian paths, providing upper bounds and developing advanced inequalities for infinite-dimensional analysis.
Contribution
It introduces new upper bounds on mean square displacement for Brownian paths under bounded pair potentials and extends key inequalities to infinite dimensions.
Findings
Derived upper bounds on mean square displacement
Developed infinite-dimensional inequalities for Brownian analysis
Applied results to study effects of pair potentials on Brownian motion
Abstract
We study Brownian paths perturbed by semibounded pair potentials and prove upper bounds on the mean square displacement. As a technical tool we derive infinite dimensional versions of key inequalities that were first used in [Sellke; arXiv:2212.14023] in order to study the effective mass of the Fr\"ohlich polaron.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Stochastic processes and statistical mechanics · Nonlinear Partial Differential Equations