Work

Functional limit theorems for perturbed random walks

Year: 2026

Type: preprint

Abstract: We consider scaling limits of integer-valued random walks whose transition probabilities are translation-invariant everywhere except on a set that we will call a membrane or an interface. If the jumps outside the membrane are i.i.d. mean-zero random variables with finite variance, then possible examples of the corresponding limit processes include reflected Brownian motion, skew Brownian motion, and Brownian motion with a jump-type exit from zero. We also discuss the question of what the possible limits are if the jumps outside the membrane belong to the domain of attraction of a stable law.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.17262

Author: Pilipenko, Andrey

Institutions: University of Geneva, National Academy of Sciences of Ukraine, Institute of Mathematics

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: Geometric and multiscale numerical methods for differential equations, Isaac Newton Institute for Mathematical Sciences (INI), G2259086438, Algebra, Analysis, Geometry and Physics, Stochastic dynamical systems with singularities, Numerical Analysis, G5599649393, G628552264

OpenAlex ID: W7213402268

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