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A branching random walk is a system of particles, where each particle gives birth to new particles of the next generation, which move on $\mathbb R^d$ according to some probability law. In this talk, ...
Let $(g_n)_{n\geq 1}$ be a sequence of independent and identically distributed random matrices of type $d \times d $ with real coefficients. Consider the products $G_n : = g_n \ldots g_1$ and the rand...
The workshop will explore large-N asymptotics of random matrices, in connection with the operator-algebra models of their limiting behavior that appear in free probability theory. The behavior or rand...
On the Eigenvalues of Random Matrices.
.L.et 1% be a random r~x r~unitary matrix with distribution given by Haar measure on the unitary group. Using explicit monlerlt calculations, a general criterion is given for linear cornbinations of...
Random Matrices, Magic Squares and Matching Polynomials。
It is a classical result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n \times n$ gaussian matrix with independent entries of mean zero and unit variance are asymp...
The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of...
Abstract: In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous determini...
Abstract: In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n...
This paper is concerned with the asymptotic behavior of the free energy for a class of Hermitean random matrix models, with odd degree polynomial potential, in the large N limit. It continues an inves...
Let A be an n random matrix with iid entries over a finite field of order q. Suppose that the entries do not take values in any additive coset of the field with probability greater than 1 − ...
For fixed m > 1, we consider m independentn non-Hermitian random matrices X1, . . . ,Xm with i.i.d. centered entries with a finite (2 + )-th moment,  > 0. As n tends to infinity, we show that the...
We consider products of independent random matrices with independent entries.The limit distribution of the expected empirical distribution of eigenvalues of such products is computed. Let X()jk , 1 ≤...
We consider powers of random matrices with independent entries. Let Xij , i, j ≥ 1,be independent complex random variables with EXij = 0 and E|Xij |2 = 1 and let X denote an n matrix with [X]ij = Xi...

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