Mészáros, András (2020) The Distribution of Sandpile Groups of Random Regular Graphs. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. pp. 167. ISSN 00029947 (print); 10886850 (online)

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Abstract
We study the distribution of the sandpile group of random dregular graphs. For the directed model, we prove that it follows the CohenLenstra heuristics, that is, the limiting probability that the pSylow subgroup of the sandpile group is a given pgroup P, is proportional to  Aut(P)−1. For finitely many primes, these events get independent in the limit. Similar results hold for undirected random regular graphs, where for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne. This answers an open question of Frieze and Vu whether the adjacency matrix of a random regular graph is invertible with high probability. Note that for directed graphs this was recently proved by Huang. It also gives an alternate proof of a theorem of Backhausz and Szegedy. This answers an open question of Frieze and Vu whether the adjacency matrix of a random regular graph is invertible with high probability. Note that for directed graphs this was recently proved by Huang. It also gives an alternate proof of a theorem of Backhausz and Szegedy.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika > QA166QA166.245 Graphs theory / gráfelmélet 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  18 Aug 2020 10:54 
Last Modified:  21 Apr 2023 09:53 
URI:  http://real.mtak.hu/id/eprint/112305 
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