We present an algorithm, based on the iteration of conformal maps, that produces independent samples of self-avoiding paths in the plane. It is a discrete process approximating radial Schramm-Loewner evolution growing to infinity. We focus on the problem of reproducing the parametrization corresponding to that of lattice models, namely self-avoiding walks on the lattice, and we propose a strategy that gives rise to discrete paths where consecutive points lie an approximately constant distance apart from each other. This new method allows us to tackle two non-trivial features of self-avoiding walks that critically depend on the parametrization: the asphericity of a portion of chain and the correction-to-scaling exponent.
Exact Sampling of Self-avoiding Paths via Discrete Schramm-Loewner Evolution / M. Gherardi. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 140:6(2010), pp. 1115-1129.
Titolo: | Exact Sampling of Self-avoiding Paths via Discrete Schramm-Loewner Evolution |
Autori: | |
Parole Chiave: | Exact sampling; Natural parametrization; Schramm-Loewner evolution; Self-avoiding walk; Mathematical Physics; Statistical and Nonlinear Physics |
Settore Scientifico Disciplinare: | Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici |
Data di pubblicazione: | 2010 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s10955-010-0031-8 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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