Stochastic version of the Erdos-Renyi limit theorem

2001/03/07 by A. Khorunzhy, Khorunzhy, A.
Mathematics · Physics and Astronomy · #05C80 #15A52 (secondary) #60F99 (primary) #FOS: Mathematics #Probability (math.PR) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR #math.SP #msc:05C80 #msc:15A52 #msc:60F99

paper · pdf · doi:10.48550/arxiv.math/0103043

LaTeX, 8 pages

openalex publication_date 2001/03/07 · arxiv created 2002/05/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalise the Erdos-Renyi limit theorem on the maximum of the partial sums of random variables to the case when the number of terms in these sums is randomly distributed. Certain relations between the limiting theorems of this type and the spectral theory of random graphs and random matrices are discussed.

Related

• Limit Theorem for Sums of Random Products
• Limiting Distributions of Sums with Random Spectral Weights
• The Entropic Erdős-Kac Limit Theorem
• The limit theorem for maximum of partial sums of exchangeable random variables
• Limiting empirical spectral distribution for the non-backtracking matrix of an Erdős-Rényi random graph