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Component sizes of the random graph outside the scaling window.
Congruence properties of depths in some random trees.
Recurrence of simple random walk on Z2 is dynamically sensitive.
We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple ap...
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory e...
The study of effective interface models has been quite active recently, with a particular emphasis on the effect of various external potentials (wall, pinning potential, ...) leading to localization/d...
We study large Wigner random matrices in the case when the marginal distributions of matrix entries have heavy tails. We prove that the largest eigenvalues of such matrices have Poisson statistics.
Chung, Diaconis, and Graham considered random processes of the form Xn+1=2Xn+bn (mod p) where X0=0, p is odd, and bn for n=0, 1, 2, ... are i.i.d. random variables on {-1,0,1}. If Pr(bn=-1)=Pr(bn=1)= ...
Let U(N) denote the maximal length of arithmetic progressions in a random uniform subset of {0,1}N. By an application of the Chen-Stein method, we show that U(N)- 2 log(N)/log(2) converges in law to a...
This note extends Voiculescu's S-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right i...
Consider the matrix Δn = (( I(Xi + Xj > 0) ))i,j =1,2,...,n where Xi are i.i.d. and their distribution is continuous and symmetric around 0. We show that the rank rn of this matrix is equal in dist...
Consider the matrix Δn = (( I(Xi + Xj > 0) ))i,j =1,2,...,n where Xi are i.i.d. and their distribution is continuous and symmetric around 0. We show that the rank rn of this matrix is equal in dist...
We show that the spectral radius of an N-dimensional random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by 2σ - o(N-6/11+ε), where σ2 ...

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