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On the Local Central Limit Theorem for Interacting Spin Systems

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Abstract

We prove the equivalence between integral and local central limit theorem for spin system interacting via an absolutely summable pair potential without any conditions on the temperature of the system.

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Acknowledgements

A. P. has been partially supported by the Brazilian science foundations Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG), B. S. acknowledges the MIUR Project awarded to the Department of Mathematics of the University of Rome “Tor Vergata”, MAT_ECCELLENZA_2023_27.

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Authors and Affiliations

  1. Departamento de Matemática UFMG, Caixa Postal 1621, Belo Horizonte, 30161-970, Brazil

    Aldo Procacci

  2. Dipartimento di Matematica Universitá di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133, Roma, Italy

    Benedetto Scoppola

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  1. Aldo Procacci
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  2. Benedetto Scoppola
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Correspondence to Aldo Procacci.

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Procacci, A., Scoppola, B. On the Local Central Limit Theorem for Interacting Spin Systems. Ann. Henri Poincaré (2024). https://doi.org/10.1007/s00023-024-01433-2

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