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

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  • Duplantier, Bertrand

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.

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  • Duplantier, Bertrand, 1992. "Loop-erased self-avoiding walks in two dimensions: exact critical exponents and winding numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 516-522.
    • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:516-522
    DOI: 10.1016/0378-4371(92)90575-B
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