Geodesic
On a Cohen-Lenstra heuristic for Jacobians of random graphs
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 701-723.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In this paper, we make specific conjectures about the distribution of Jacobians of random graphs with their canonical duality pairings. Our conjectures are based on a Cohen-Lenstra-type heuristic saying that a finite abelian group with duality pairing appears with frequency inversely proportional to the size of the group times the size of the group of automorphisms that preserve the pairing. We conjecture that the Jacobian of a random graph is cyclic with probability a little over .7935. We determine the values of several other statistics on Jacobians of random graphs that would follow from our conjectures. In support of the conjectures, we prove that random symmetric matrices over $\mathbb Z_p$, distributed according to Haar measure, have cokernels distributed according to the above heuristic. We also give experimental evidence in support of our conjectures.
Classification : 05C80
Keywords: random graphs, Cohen-Lenstra heuristics, cokernels of random matrices, sandpile groups, graph Jacobians 
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     title = {On a {Cohen-Lenstra} heuristic for {Jacobians} of random graphs},
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Clancy, Julien; Kaplan, Nathan; Leake, Timothy; Payne, Sam; Matchett Wood, Melanie. On a Cohen-Lenstra heuristic for Jacobians of random graphs. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 701-723. http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a9/