Work

On Local Large Deviations for Decoupled Random Walks

Year: 2026

Type: article

Abstract: A decoupled standard random walk is a sequence of independent random variables $$(\hat{S}_n)_{n \ge 1}$$ such that, for each $$n \ge 1$$ , the distribution of $$\hat{S}_n$$ is the same as that of $$S_n = \xi _1 + \ldots + \xi _n$$ , where $$(\xi _k)_{k \ge 1}$$ are independent copies of a nonnegative random variable $$\xi $$ . We consider the counting process $$(\hat{N}(t))_{t\ge 0}$$ defined as the number of terms $$\hat{S}_n$$ in the sequence $$(\hat{S}_n)_{n \ge 1}$$ that lie within the interval [0, t]. Under various assumptions on the tail distribution of $$\xi $$ , we derive logarithmic asymptotics for the local large deviation probabilities $$P{\hat{N}(t) = \lfloor bE[\hat{N}(t)]}$$ as $$t \rightarrow \infty $$ for a fixed constant $$b>0$$ . These results are then applied to obtain a logarithmic local large deviations asymptotic for the counting process associated with the infinite Ginibre ensemble and, more generally, for determinantal point processes with the Mittag-Leffler kernel.

Source: Journal of Statistical Physics

DOI: 10.1007/s10955-026-03715-x

Authors: Dariusz Buraczewski, Alexander Iksanov, Alexander Marynych

Institutions: Taras Shevchenko National University of Kyiv, Kyiv School of Economics

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Narodowym Centrum Nauki, Uniwersytet Wrocławski