Transition of the Simple Random Walk on the Ice Model Graph

Xavier Bressaud and Serge Cohen ()
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Xavier Bressaud: Université de Toulouse, CNRS, UT3
Serge Cohen: Université de Toulouse, CNRS, UT3

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3455-3478

Abstract: Abstract The 6-vertex model holds significance in various mathematical and physical domains. The configurations of the 6-vertex model correspond to the paths in multigraphs. This article focuses on calculating the transition probability for the simple random walk on these multigraphs. An intriguing aspect of the findings is the utilization of continued fractions in the computation of the transition probability.

Keywords: Random walk; Markov chain; Square ice model; 6-vertex model; Height functions; Thermodynamic limit; Continued Fractions; 05C81; 60J10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01357-x

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