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Logarithmic Sobolev inequality for generalized simple exclusion processes
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  • Published: November 1997

Logarithmic Sobolev inequality for generalized simple exclusion processes

  • Horng-Tzer Yau1 

Probability Theory and Related Fields volume 109, pages 507–538 (1997)Cite this article

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Summary.

Let be a probability measure on the set {0,1, . . .,R} for some R∈ℕ and Λ L a cube of width L in ℤ d. Denote by μgc ΛL the (grand canonical) product measure on the configuration space on Λ L with as the marginal measure; here the superscript indicates the grand canonical ensemble. The canonical ensemble, denoted by μc ΛL,n , is defined by conditioning μgc ΛL given the total number of particles to be n. Consider the exclusion dynamics where each particle performs random walk with rates depending only on the number of particles at the same site. The rates are chosen such that, for every n and L fixed, the measure μc ΛL,n is reversible. We prove the logarithmic Sobolev inequality in the sense that ∫flogfdμc ΛL,n ≤ for any probability density f with respect to μc ΛL,n ; here the constant is independent of n or L and D denotes the Dirichlet form of the dynamics. The dependence on L is optimal.

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Authors and Affiliations

  1. Courant Institute, New York University New York, NY 10012, USA e-mail: yau@math.nyu.edu , , , , , , US

    Horng-Tzer Yau

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  1. Horng-Tzer Yau
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Received: 22 May 1996 / In revised Form: 7 March 1997

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Yau, HT. Logarithmic Sobolev inequality for generalized simple exclusion processes. Probab Theory Relat Fields 109, 507–538 (1997). https://doi.org/10.1007/s004400050140

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  • Issue Date: November 1997

  • DOI: https://doi.org/10.1007/s004400050140

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Keywords

  • Probability Density
  • Probability Measure
  • Random Walk
  • Configuration Space
  • Product Measure
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