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19972026
most citedEfficient Behavior of Small-World Networks

5.1k citations

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Showing 2020 · math-phShow all

5 papers · 2 filters

math-ph2020★ 12 cited

Statistical properties of structured random matrices

Eugene Bogomolny, Olivier Giraud

Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical a…

math-ph2020

A shifted binomial theorem and trigonometric series

Stéphane Ouvry, Alexios P. Polychronakos

We introduce a shifted version of the binomial theorem, and use it to study some remarkable trigonometric integrals and their explicit rewriting in terms of binomial multiple sums.…

math-ph2020★ 1 cited

Tracy-Widom distributions for the Gaussian orthogonal and symplectic ensembles revisited: a skew-orthogonal polynomials approach

Anthony Mays, Anita Ponsaing, Gregory Schehr

We study the distribution of the largest eigenvalue in the "Pfaffian" classical ensembles of random matrix theory, namely in the Gaussian orthogonal (GOE) and Gaussian symplectic (…

math-ph2020

Lattice walk area combinatorics, some remarkable trigonometric sums and Apéry-like numbers

Stéphane Ouvry, Alexios Polychronakos

Explicit algebraic area enumeration formulae are derived for various lattice walks generalizing the canonical square lattice walk, and in particular for the triangular lattice chir…

math-ph2020★ 7 cited

Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity

Aurélien Grabsch, Christophe Texier

We consider a multichannel wire with a disordered region of length and a reflecting boundary. The reflection of a wave of frequency is described by the scattering matrix $\…