Development and regression of a large fluctuation.

We study the evolution leading to (or regressing from) a large fluctuation in a statistical mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables n_{m} (m=1,M) evolving by means of a master equation. We show that the process producing a nontypical fluctuation with a value of N=∑_{m=1}^{M}n_{m} well above the average 〈N〉 is slow. Such process is characterized by the power-law growth of the largest possible observable value of N at a given time t. We find similar features also for the reverse process of the regression from a rare state with N≫〈N〉 to a typical one with N≃〈N〉.