End patterns of self-avoiding walks

Journal Article · Tue Nov 01 04:00:00 EST 1988 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01014220· OSTI ID:6279419

Madras, N

Consider a fixed end pattern (a short self-avoiding walk) that can occur as the first few steps of an arbitrarily long self-avoiding walk on Z/sup d/. It is a difficult open problem to show that as N ..-->.. infinity, the fraction of N-step self-avoiding walks beginning with this pattern converges. It is shown that as N ..-->.. infinity, this fraction is bounded away from zero, and that the ratio of the fractions for N and N + 2 converges to one. Similar results are obtained when patterns are specified at both ends, and also when the endpoints are fixed.

• Research Organization: York Univ., Ontario (Canada)
• OSTI ID: 6279419
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Journal Issue: 3-4 Vol. 53:3-4; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
BOUNDARY CONDITIONS
CONVERGENCE
ERGODIC HYPOTHESIS
HYPOTHESIS
MAPPING
MATHEMATICAL LOGIC
MATHEMATICAL MANIFOLDS
MECHANICS
MONTE CARLO METHOD
PROBABILITY
RANDOMNESS
STATISTICAL MECHANICS
TOPOLOGICAL MAPPING
TRANSFORMATIONS