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math.PR2026
On Anti-Confinement Estimates for Self-Repelling Random Walks
Tobias Schmidt, Mark Sellke
We study a class of -dimensional random walks, including the two-dimensional simple random walk, reweighted by a self-repelling Gibbsian pair potential. We prove lower bounds on…
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.