Kavitha, Veeraruna Altman, Eitan

Many systems require frequent and regular updates of certain information. These updates have to be transferred regularly from the source(s) to a common destination. We consider scenarios in which an old packet (entire information unit) becomes completely obsolete, in the presence of a new packet. We consider transmission channels with unit storage ...

Chitour, Yacine Mazanti, Guilherme Sigalotti, Mario

Given a discrete-time linear switched system $\Sigma(\mathcal A)$ associated with a finite set $\mathcal A$ of matrices, we consider the measures of its asymptotic behavior given by, on the one hand, its deterministic joint spectral radius $\rho_{\mathrm d}(\mathcal A)$ and, on the other hand, its probabilistic joint spectral radii $\rho_{\mathrm p...

Bercu, Bernard Laulin, Lucile

Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its whole history. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratric strong law for the cente...

Grusea, Simona Labarre, Anthony

The prefix exchange distance of a permutation is the length of its shortest factorisation into transpositions that all contain 1. Using a probabilistic approach, we obtain expressions for the mean and the variance, and prove the asymptotic normality of the distribution of this distance for a random permutation verifying the Ewens sampling formula. ...

Loubaton, Philippe Mestre, Xavier

Barraquand, Guillaume Krajenbrink, Alexandre Doussal, Pierre Le

We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line, equivalently the free energy of the continuum directed polymer in a half space with a wall at $x=0$. The boundary condition $\partial_x h(x,t)|_{x=0}=A$ corresponds to an attractive wall for $A0$ wi...

Morin, Léo Mouzard, Antoine

We define the random magnetic Laplacien with spatial white noise as magnetic field on the two-dimensional torus using paracontrolled calculus. It yields a random self-adjoint operator with pure point spectrum and domain a random subspace of nonsmooth functions in L 2. We give sharp bounds on the eigenvalues which imply an almost sure Weyl-type law....

Avrachenkov, Konstantin Mironov, Maksim

In this paper we consider a graph clustering problem with a given number of clusters and approximate desired sizes of the clusters. One possible motivation for such task could be the problem of databases or servers allocation within several given large computational clusters, where we want related objects to share the same cluster in order to minim...

Beiglböck, Mathias Jourdain, Benjamin Margheriti, William Pammer, Gudmund

Our main result is to establish stability of martingale couplings: suppose that $\pi$ is a martingale coupling with marginals $\mu, \nu$. Then, given approximating marginal measures $\tilde \mu \approx \mu, \tilde \nu\approx \nu$ in convex order, we show that there exists an approximating martingale coupling $\tilde\pi \approx \pi$ with marginals $...

Merlevède, Florence Najim, Jamal Tian, Peng

Given a large sample covariance matrix $S_N=\frac 1n\Gamma_N^{1/2}Z_N Z_N^*\Gamma_N^{1/2}\, ,$ where $Z_N$ is a $N\times n$ matrix with i.i.d. centered entries, and $\Gamma_N$ is a $N\times N$ deterministic Hermitian positive semidefinite matrix, we study the location and fluctuations of $\lambda_{\max}(S_N)$, the largest eigenvalue of $S_N$ as $N,...