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On the Renormalization Group Method for the Problem of Random Walk without Self‐Intersections
Author(s) -
Alkhimov V. I.
Publication year - 1984
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19844960310
Subject(s) - renormalization group , random walk , heterogeneous random walk in one dimension , euclidean space , statistical physics , space (punctuation) , physics , mathematics , euclidean geometry , probability density function , group (periodic table) , mathematical physics , mathematical analysis , statistics , quantum mechanics , geometry , computer science , operating system
Random walk without self‐intersections for a particle in the Euclidean n ‐dimensional space is investigated. Renormalization group equations for the probability density of the end‐to‐end distance of a particle trajectory are derived. The asymptotics for this probability density are defined for 4 ‐ n ≪ 1.