THE SELF-AVOIDING WALK

By JA. Sanchez. 2006

845 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8516841402e10b2b37064ab48888da06cf806ab9

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Citations in the corpus

Random subgraphs of finite graphs : II. The lace expansion and the triangle condition (2004, methodology): “Since the late 1980s, lace expansion methods have been used to derive detailed estimates on the critical behaviour of several models in high dimensions; see [14, 21, 25] for reviews.”
Towards conformal invariance of 2D lattice models (2007, background): “For their interrelations and for the discussion of many other relevant models one can consult the books [6], [12], [26], [27].”
Polymers with spatial or topological constraints: Theoretical and computational results (2011, methodology): “Because at each Monte Carlo step, the probability of accepting the trial configuration depends only on the configuration at the previous step (and not on “older” ones), the MC evolution realizes a Markov chain [90, 92, 93] Starting from an initial conformation, the repeated application of the accept”
Intersections of random walks (2011, background): “They play a key role e.g. in description of polymer chains (Madras and Slade [MS93]).”
Random walks and diffusion on networks (2016, background): “RWs [4, 70, 71], zero-range processes [72], multiplicative random processes [73, 105 74], adaptive RWs (including reinforced RWs [75]), branching RWs [76], Lévy 106 flights [34, 35], elephant RWs [77], quantum walks [78, 79], intermittent RWs 107 [80], persistent RWs [81], starving RWs [82–84], mort”
Conformally invariant scaling limits: an overview and a collection of problems (2006, background): “See [67] for references and further background on the self-avoiding walk.”
The Random-Cluster Model (2002, methodology): “t for Potts models, [104], which may be used to show ﬁrst-order phase transition when qis suﬃciently large. Let a n be the number of self-avoiding walks on L2 beginning at the origin. It is standard, [114], that a1/n n → µ as n → ∞, for some constant µ called the connective constant of the lattice. ”
Conformally Invariant Processes in the Plane (2005, background): “As an example of results in this direction see [1, 7, 20, 25, 45].”
The Lace Expansion and its Applications (2006, methodology): “The same result is obtained in [158] for the spread-out model in dimensions d > 4 with L sufficiently large.”