Title: Information percolation and cutoff for the Glauber-Exclusion process. Abstract: The Glauber-Exclusion process, an interacting particle system introduced by De Masi, Ferrari, and Lebowitz, is a superposition of a Glauber dynamics and the symmetric simple exclusion process (SSEP) on a…
Title: Resilience of cube slicing in $\ell_p$ Abstract: We shall discuss the state of the art on the problem of identifying the volume maximizing and minimizing hyperplane sections of $p$-balls in $\mathbb{R}^n$. After explaining a reduction to a sharp probabilistic…
Title: High-temperature cluster expansion for quantum spin lattice systems Abstract: We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum —and, in particular, classical— interactions. Our approach is based on the use of the M ̈obius…
Title: Infinitesimal Freeness Abstract: A universal rule for computing mixed moments of independent and unitarily invariant random matrices gives, in the large N limit, the rule for free independence. In the forty years since Voiculescu gave this rule many extensions…
Title: The probabilistic construction of the two-dimensional sinh model in quantum field theory
Title: (Towards an) Invariance Principle for the Random Lorentz Gas under Weak Coupling Limit Beyond the Kinetic Time Scale Abstract: Kesten-Papanicolaou (1980) proved that in the weak coupling limit the random Lorentz-gas process with soft scatterers converges to the Spherical Langevin Process.…
Title: Spectrum of Linial-Meshulam complex in thermodynamic regime Abstract: Linial-Meshulam complex, denoted by , is a random simplicial complex on vertices with a complete -dimensional skeleton and -simplices chosen independently with probability . Linial-Meshulam complex is one of the most studied generalizations of the Erdos-Renyi random…
Title: Permutation matrices, graph independence over the diagonal, and consequences Abstract: Often, one tries to understand the behaviour of non-commutative random variables or of von Neumann algebras through matricial approximations. In some cases, such as when appealing to the determinant…
Title: Limits of finite trees Abstract: Motivated by the work of Lovász, Szegedy and others on the convergence and limits of dense graph sequences, we investigate the convergence and limits of finite trees with respect to sampling in normalized distance.…
Title: The spectral edge of constant degree Erdős-Rényi graphs Abstract: Determining the spectrum and eigenvectors of the adjacency matrix of random graphs is a fundamental problem with applications in computer science and statistical physics. Often, the relevant model is…
Title: A new approach to proving strong convergence of random matrices Abstract. Friedman's celebrated 2004 result states that, as the number of vertices goes to infinity, random d-regular graphs are (with high probability) nearly optimal expanders, meaning that the top…