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Fundamental constants in the theory of two-dimensional uniform spanning trees
V. S. Pogosyanab, V. B. Priezzheva a Bogoliubov Laboratory of Theoretical Physics, Joint
Institute for Nuclear Research, Dubna, Russia
b Institute for Informatics and Automation Problems, National
Academy of Sciences of Armenia, Yerevan, Armenia
Abstract:
Three characteristics of two-dimensional uniform spanning trees are
nontrivially related to one another{:} the average density of a sandpile,
the looping constant of a square lattice, and the return probability of a loop-erased random walk. We briefly trace the long history of the discovery
of their unexpected rational values.
Keywords:
Abelian sandpile model, loop-erased random walk, monomer–dimer model.
Received: 28.12.2015
Citation:
V. S. Pogosyan, V. B. Priezzhev, “Fundamental constants in the theory of two-dimensional uniform spanning trees”, TMF, 187:3 (2016), 580–594; Theoret. and Math. Phys., 187:3 (2016), 952–963
Linking options:
https://www.mathnet.ru/eng/tmf9136https://doi.org/10.4213/tmf9136 https://www.mathnet.ru/eng/tmf/v187/i3/p580
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Abstract page: | 318 | Full-text PDF : | 134 | References: | 44 | First page: | 24 |
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