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تسجيل مستخدم جديدNoncrossing partition flow and random matrix models
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تأليف
Mario Pernici
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We study a generating function flowing from the one enumerating a set of partitions to the one enumerating the corresponding set of noncrossing partitions; numerical simulations indicate that its limit in the Adjacency random matrix model on bipartite Erdos-Renyi graphs gives a good approximation of the spectral distribution for large average degrees. This model and a Wishart-type random matrix model are described using congruence classes on $k$-divisible partitions. We compute, in the $dto infty$ limit with $frac{Z_a}{d}$ fixed, the spectral distribution of an Adjacency and of a Laplacian random block matrix model, on bipartite Erdos-Renyi graphs and on bipartite biregular graphs with degrees $Z_1, Z_2$; the former is the approximation previously mentioned; the latter is a mean field approximation of the Hessian of a random bipartite biregular elastic network; it is characterized by an isostatic line and a transition line between the one- and the two-band regions.
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