Distribution of levels in high-dimensional random landscapes

DOI10.1214/11-AAP772zbMath1246.60036arXiv1005.3207MaRDI QIDQ2428053

Zakhar Kabluchko

Publication date: 20 April 2012

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.3207

zbMATH Keywords

disordered systemscentral limit theoremlong-range dependenceempirical process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items

Asymptotic expansions in the central limit theorem for a branching Wiener process, A second order asymptotic expansion in the local limit theorem for a simple branching random walk in \(\mathbb{Z}^d\), First- and second-order expansions in the central limit theorem for a branching random walk, Edgeworth expansions for profiles of lattice branching random walks, General Edgeworth expansions with applications to profiles of random trees, Exact convergence rates for particle distributions in a non-lattice branching random walk, Exact convergence rate of the local limit theorem for branching random walks on the integer lattice, Unnamed Item, Exact convergence rates in central limit theorems for a branching random walk with a random environment in time, Fluctuations for the partition function of Ising models on Erdös-Rényi random graphs, Exact convergence rate of the local limit theorem for a branching random walk in a time-dependent random environment on d-dimensional integer lattice

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local energy statistics in spin glasses
• The empirical process of some long-range dependent sequences with an application to U-statistics
• Convergence of empirical processes of mixing rv's on \([0,1\)]
• A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences
• A note on empirical processes of strong-mixing sequences
• Exact convergence rates for the distribution of particles in branching random walks
• Probability on Trees and Networks
• Proof of the local REM conjecture for number partitioning. I: Constant energy scales
• Proof of the local REM conjecture for number partitioning. II. Growing energy scales
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
• A Local Limit Theorem for Nonlattice Multi-Dimensional Distribution Functions
• Occupation times of stationary gaussian processes