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We study the distribution of the sandpile group of random d-regular graphs.
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Russel Lyons. Asymptotic Enumeration of Spanning Trees, Combin. Probab. Comput. 14 (2005), 491-522
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Lionel Levine and James Propp. What is … a sandpile? Notices Amer. Math. Soc., 57(8):976-979, 2010
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Serguei Norine and Peter Whalen. Jacobians of nearly complete and threshold graphs. European Journal of Combinatorics, 32(8):1368-1376, November 2011
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A. Frieze. Random structures and algorithms. In Proceedings of the International Congress of Mathematicians-Seoul 2014. Vol. 1, pages 311-340. Kyung Moon Sa, Seoul, 2014
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Miklós Abért, ’Graph convergence, Luck approximation mod p and the entropy of cellular automata’, Growth, symbolic dynamics and combinatorics of words in groups, June 2, 2015, ENS, Paris, video available at https://www.youtube.com/watch?v=wRRFOGPnaJY
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Rémi Bardenet, Odalric-Ambrym Maillard, Concentration inequalities for sampling without replacement, Bernoulli 21 (2015), no. 3, 13611385
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Matthew Farrell and Lionel Levine. CoEulerian graphs. Proceedings of the American Mathematical Society, 2015
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Shaked Koplewitz. Sandpile groups and the coEulerian property for random directed graphs, Advances in Applied Mathematics, 2017
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2013
Cited alongside, same era.
2013
Cited alongside, same era.
Julien Clancy, Timothy Leake, Nathan Kaplan, Sam Payne, and Melanie Matchett Wood. On a cohen-lenstra heuristic for jacobians of random graphs. 2014. preprint
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Cited in the paper.
Thomas M. Cover, Joy A. Thomas, Elements of Information Theory, 2nd Edition (Wiley Series in Telecommunications and Signal Processing)
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William Feller, An Introduction to Probability Theory and its Applications ( Volume 1 ), 2nd Edition, John Wiley & Sons Inc
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Alexander E. Holroyd, Lionel Levine, Karola Mészáros, Yuyal Peres, James Propp, and David B. Wilson. Chip-firing and rotor-routing on directed graphs. In Vladas Sidoravicius and Maria Eulália Vares, editors, In and Out of Equilibrium 2, volume 60, pages 331-364. Birkhauser Basel, Basel
Cited in the paper.
2017
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Melanie Matchett Wood, The distribution of sandpile groups of random graphs, Journal of the American Mathematical Society 30 (2017), pp. 915-958
2017
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Antal A. Járai, Sandpile models, Probability Surveys, Volume 15 (2018), 243-306
2018
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Melanie Matchett Wood, Personal communication, 2018
2018
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