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math.PR2025
Sub-diffusive regimes for long range self-interacting path measures
Volker Betz, Tobias Schmidt, Mark Sellke
We study Brownian motion perturbed by a long range self-interaction. We provide variance bounds in terms of the spatial interaction strength and the order of time decay.
math.PR2023
Mean square displacement of Brownian paths perturbed by bounded pair potentials
Volker Betz, Tobias Schmidt, Mark Sellke
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…