Moderate deviations for the capacity of the random walk range in dimension four
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
Fields of Study & Subjects
Mathematical Approximation and Integration
Stochastic processes and statistical mechanics
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- The Annals of Probability
- Publisher
- Institute of Mathematical Statistics
- Volume
- 54
- Issue
- 4
- Pages
- 1641-1685
- Publication date
- 30 June 2026
- Language
- EN