Frigio, S. and Poghosyan, S. K. (2007) *Asymptotics of Brownian Integrals and Pressure. Bose-Einstein Statistics.* Հայաստանի ԳԱԱ Տեղեկագիր. Մաթեմատիկա, 42 (3). pp. 23-38. ISSN 00002-3043

## Abstract

The paper studies the asymptotics of the Brownian integrals with paths restricted to a bounded domain of R, when the domain is dilated to infinity. The framework is that of the Bose-Einstein statistics with paths observed within random time intervals which are integer multiplies of some fixed β > 0. The three first terms of the asymptotics are found explicitly via the functional integrals. In the case of a gas of interacting Brownian loops an expression for the volume term of the asymptotics of the log-partition function is found and the correction term is proved to by order be the boundary area of the domain.

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