FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 5, PAGES 3-20

**Asymptotic distribution of the size of
a $d$-dimensional model of an open string**

V. I. Alkhimov

Abstract

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In this paper, we propose a statistical description of the
configuration of a $d$-dimensional model of an
open string that avoids self-intersection.
For the distribution of the distance between the ends of the string we
have obtained an exact integral equation similar to the well-known
Dyson equation in quantum field theory.
The resulting equation is invariant under continuous transformations
of the renormalization group, which allows one to use the
renormalization group method to establish the desired asymptotic
distribution.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k115/k11501h.htm

Last modified: October 18, 2012