Return probability for the loop-erased random walk and mean height in the Abelian sandpile model: a proof
Year: 2011
Type: article
Abstract: Single site height probabilities in the Abelian sandpile model, and the corresponding mean height ⟨ h ⟩, are directly related to the probability P ret that a loop-erased random walk passes through a nearest neighbour of the starting site (return probability). The exact values of these quantities on the square lattice have been conjectured, in particular ⟨ h ⟩ = 25/8 and P ret = 5/16. We provide a rigorous proof of this conjecture by using a local monomer–dimer formulation of these questions.
Authors: Vahagn S Poghosyan, Vyatcheslav B Priezzhev, Philippe Ruelle
Institutions: UCLouvain, Joint Institute for Nuclear Research
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G7749338082, G7925923548
OpenAlex ID: W1575809656