FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 2, PAGES 3-21

**Random process in a homogeneous Gaussian field**

V. I. Alkhimov

Abstract

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We consider a random process in a spatial-temporal
homogeneous Gaussian field $V($**q**,t) with the mean
$$**E**V=0 and the
correlation function $W(|$**q** - **q**'|,|t -
t'|) º
**E**[V(**q**,t)V(**q**',t')], where $$**q** Î
**R**^{d}, $t$Î
**R**^{+}, and $d$ is the dimension of the
Euclidean space $$**R**^{d}.
For a "density" $G(r,t)$ of the familiar
model of a physical system averaged over all realizations of the
random field $V$, we establish an integral
equation which has the form of the Dyson equation.
The invariance of the equation under the continuous renormalization
group allows using the renormalization group method to find an
asymptotic expression for $G(r,t)$ as $r\; \to $¥ and $t\; \to $¥.

Location: http://mech.math.msu.su/~fpm/eng/k09/k092/k09201h.htm

Last modified: December 22, 2009