| Автор | Poghosyan, Vahagn S |
| Автор | Priezzhev, Vyatcheslav B |
| Автор | Ruelle, Philippe |
| Дата выпуска | 2011-10-01 |
| dc.description | Single site height probabilities in the Abelian sandpile model, and the corresponding mean height ⟨h⟩, are directly related to the probability P<sub>ret</sub> 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<sub>ret</sub> = 5/16. We provide a rigorous proof of this conjecture by using a local monomer–dimer formulation of these questions. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Копирайт | IOP Publishing Ltd |
| Название | Return probability for the loop-erased random walk and mean height in the Abelian sandpile model: a proofWe are delighted to dedicate this work to Deepak Dhar on the occasion of his 60th birthday. |
| Тип | paper |
| DOI | 10.1088/1742-5468/2011/10/P10004 |
| Electronic ISSN | 1742-5468 |
| Журнал | Journal of Statistical Mechanics: Theory and Experiment |
| Том | 2011 |
| Первая страница | P10004 |
| Последняя страница | 11 |
| Аффилиация | Poghosyan, Vahagn S; Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, B-1348 Louvain-La-Neuve, Belgium |
| Аффилиация | Priezzhev, Vyatcheslav B; Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia |
| Аффилиация | Ruelle, Philippe; Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, B-1348 Louvain-La-Neuve, Belgium |
| Выпуск | 10 |
