Elsevier

Nuclear Physics B

Volume 374, Issue 3, 4 May 1992, Pages 720-740
Nuclear Physics B

The hole probability in log-gas and random matrix systems

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Abstract

The probability of a particle free region (i.e. hole) in a hard-core lattice gas can be written as a finite sum over the distribution functions. In the special case in which the distribution functions have a determinant structure, of which the one-component log-gas at the couplings Γ = 2 and 4 on a one-dimensional lattice and the former system near a metal wall are examples, the sum can be written as a single Toeplitz determinant. Asymptotic formulas for the hole probability in the large hole size limit can then be obtained by using known theorems regarding the asymptotics of Toeplitz determinants. A conjecture, suggested by the exact analysis, is given for the leading behaviour of this probability for a general class of fluid systems.

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    Supported by the Australian Research Council.

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