Work

Moderate deviations for the capacity of the random walk range in dimension four

Year: 2026

Type: article

Abstract: In this paper we find a natural four-dimensional analog of the moderate deviation results for the capacity of the random walk, which corresponds to Bass, Chen and Rosen (Mem. Amer. Math. Soc. 198 (2009) viii+82) concerning the volume of the random walk range for d=2. We find that the deviation statistics of the capacity of the random walk can be related to the following constant of generalized Gagliardo–Nirenberg inequalities: inff:‖∇f‖L2<∞ ‖f‖L21/2‖∇f‖L21/2 [∫(R4)2f2(x)G(x−y)f2(y)dxdy]1/4.

Source: The Annals of Probability

DOI: 10.1214/24-aop1727

Authors: Arka Adhikari, Izumi Okada

Institutions: Stanford University, Chiba University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Japan Society for the Promotion of Science

Awards: PostDoctoral Research Fellowship, Analysis of non-intersection probability of random walks using Green's function