We prove that any deterministic matrix is approximately the identity in the eigenbasis of a
large random Wigner matrix with very high probability and with an optimal error inversely …

We consider large non-Hermitian real or complex random matrices XX with independent,
identically distributed centred entries. We prove that their local eigenvalue statistics near the …

For complex Wigner-type matrices, ie Hermitian random matrices with independent, not
necessarily identically distributed entries above the diagonal, we show that at any cusp …

We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued
orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non …

Duality identities in random matrix theory for products and powers of characteristic
polynomials, and for moments, are reviewed. The structure of a typical duality identity for the …

We consider N by N deformed Wigner random matrices of the form XN= HN+ AN, where HN
is a real symmetric or complex Hermitian Wigner matrix and AN is a deterministic real …

We study uniformly random lozenge tilings of general simply connected polygons. Under a
technical assumption that is presumably generic with respect to polygon shapes, we show …

In this paper, we are concerned with the deformed Pearcey determinant det⁡(I− γ K s, ρ Pe),
where 0≤ γ< 1 and K s, ρ Pe stands for the trace class operator acting on L 2 (− s, s) with the …

This paper uses new and recently established methodologies to study the evolutionary
dynamics of the cryptocurrency market, and compares the findings with that of the equity …

The Pearcey kernel is a classical and universal kernel arising from random matrix theory,
which describes the local statistics of eigenvalues when the limiting mean eigenvalue …