Loop-erased self-avoiding walks in two dimensions: exact critical exponents and winding numbers

Bertrand Duplantier

Physica A: Statistical Mechanics and its Applications, 1992, vol. 191, issue 1, 516-522

Abstract: Loop-erased self-avoiding walks (LESAWs) are defined as walks resulting from sequential erasing of the loops of random walks. The critical properties of LESAWs are those of a c = −2 conformal theory in two dimensions, and, geometrically, those of subgraphs of spanning trees. In this paper, we derive the exact asymptotic behavior of the set of probabilities Pk(N) that k(k⩾2) LESAWs of length N starting at neighbouring points do not intersect, as well as the exact asymptotic winding angle distribution of a single two-dimensional LESAW.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:191:y:1992:i:1:p:516-522

DOI: 10.1016/0378-4371(92)90575-B

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