A Glivenko-Cantelli theorem for almost additive functions on lattices

DOI10.1016/j.spa.2016.06.005zbMath1353.60037arXiv1606.07664OpenAlexW2467576959WikidataQ59311963 ScholiaQ59311963MaRDI QIDQ347474

Fabian Schwarzenberger, Ivan Veselić, Christoph Schumacher

Publication date: 30 November 2016

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.07664

zbMATH Keywords

uniform convergencelarge deviationsstatistical mechanicsempirical measuresGlivenko-Cantelli theory

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12) Limit theorems in probability theory (60F99)

Related Items

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Cites Work

• Unnamed Item
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• A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states
• The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality
• Examples of multidimensional, almost periodic operators, whose point and continuous spectra intersect
• Uniform existence of the integrated density of states for models on \({\mathbb{Z}}^d\)
• Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence
• The empirical discrepancy over lower layers and a related law of large numbers
• Spectral analysis of percolation Hamiltonians
• Existence and regularity properties of the integrated density of states of random Schrödinger operators
• An ergodic theorem for Delone dynamical systems and existence of the integrated density of states
• Fluctuations of extensive functions of quenched random couplings
• On groups with full Banach mean value
• Asymptotic Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator
• On a generalization of the Glivenko-Cantelli theorem
• Percolation
• Uniform ergodic theorems on subshifts over a finite alphabet
• Generalizations of the Glivenko-Cantelli Theorem
• Statistical Mechanics of Disordered Systems
• Random Spin Systems: Some Rigorous Results
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
• Relations between Weak and Uniform Convergence of Measures with Applications
• Quelques Propriétés Générales De L'intégrale De Configuration D'un Système De Particules Avec Interaction