Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach |
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| Authors: | G. G. Bosco F. P. Machado Thomas Logan Ritchie |
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| Affiliation: | 1.Faculdade de Filosofia Ciências e Letras de Ribeir?o Preto,Universidade de S?o Paulo,Ribeir?o Preto,Brazil;2.Instituto de Matemática e Estatística,Universidade de S?o Paulo,S?o Paulo,Brazil;3.Universidade Federal do ABC,Santo André,Brazil |
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| Abstract: | We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in SmathbbZdS^{mathbb{Z}^{d}}, S a bounded subset of R n , is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented. |
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