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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 3, Pages 580–594
DOI: https://doi.org/10.4213/tmf9136 (Mi tmf9136) 		 
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
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DOI: https://doi.org/10.4213/tmf9136
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.
Funding agency Grant number
Russian Foundation for Basic Research 16-02-00252
The research of V. S. Poghosyan was supported by the Joint Institute for Nuclear Research Program "Smorodinsky–Ter-Antonyan. The research of V. B. Priezzhev was supported by the Russian Foundation for Basic Research (Grant No. 16-02-00252).
Received: 28.12.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 3, Pages 952–963
DOI: https://doi.org/10.1134/S0040577916060118
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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