169 citations · 2k across the 117 of their papers we have counts for
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The p-Airy distribution
Sergio Caracciolo, Vittorio Erba, Andrea Sportiello
In this manuscript we consider the set of Dyck paths equipped with the uniform measure, and we study the statistical properties of a deformation of the observable "area below the D…
Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians
Sergio Caracciolo, Alan D. Sokal, Andrea Sportiello
The classic Cayley identity states that \det(\partial) (\det X)^s = s(s+1)...(s+n-1) (\det X)^{s-1} where X=(x_{ij}) is an n-by-n matrix of indeterminates and \partial=(\partial/\p…
Noncommutative determinants, Cauchy-Binet formulae, and Capelli-type identities. I. Generalizations of the Capelli and Turnbull identities
Sergio Caracciolo, Andrea Sportiello, Alan D. Sokal
We prove, by simple manipulation of commutators, two noncommutative generalizations of the Cauchy-Binet formula for the determinant of a product. As special cases we obtain element…