Related papers: Replica Bounds by Combinatorial Interpolation for …
We study the set of possible configurations for a general kinetically constrained model (KCM), a non monotone version of the $\mathcal{U}$-bootstrap percolation cellular automata. We solve a combinatorial question that is a generalization…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
Define the scaled empirical point process on an independent and identically distributed sequence $\{Y_i: i\le n\}$ as the random point measure with masses at $a_n^{-1} Y_i$. For suitable $a_n$ we obtain the weak limit of these point…
The random energy model (REM) is the simplest spin glass model which exhibits replica symmetry breaking. It is well known since the 80's that its overlaps are non-selfaveraging and that their statistics satisfy the predictions of the…
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower…
In this paper we study the Random energy model - so called toy model of the spin glass theory - where the underlying distributions are compactly supported. We prove a general theorem on the asymptotics of free energy and obtain formulae in…
We study the universality of superconcentration for the free energy in the Sherrington-Kirkpatrick (SK) model. In arXiv:0907.3381, Chatterjee showed that when the system consists of $N$ spins and Gaussian disorders, the variance of this…
Diluted mean-field models are spin systems whose geometry of interactions is induced by a sparse random graph or hypergraph. Such models play an eminent role in the statistical mechanics of disordered systems as well as in combinatorics and…
We consider the number of common edges in two independent random spanning trees of a graph $G$. For complete graphs $K_n$, we give a new proof of the fact, originally obtained by Moon, that the distribution converges to a Poisson…
This article completes [G. Giacomin, R. Greenblatt, ALEA 2022] by identifying explicitly the leading coefficient in the asymptotic development of the free energy density of the centered Random Field Ising Chain as the spin-spin interaction…
In [Schuhmacher, Electron. J. Probab. 10 (2005), 165--201] estimates of the Barbour-Brown distance d_2 between the distribution of a thinned point process and the distribution of a Poisson process were derived by combining discretization…
These expository notes are centered around the circular law theorem, which states that the empirical spectral distribution of a nxn random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex…
We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica…
Many phenomena can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction…
For $n\ge 1$, let $T_n$ be a random recursive tree on the vertex set $[n]=\{1,\ldots,n\}$. Let $\mathrm{deg}_{T_n}(v)$ be the degree of vertex $v$ in $T_n$, that is, the number of children of $v$ in $T_n$. Devroye and Lu showed that the…
Motivated by recent experiments with two-component Bose-Einstein condensates, we study fully-connected spin models subject to an additional constraint. The constraint is responsible for the Hilbert space dimension to scale only linearly…
We discuss a generalization of the conditions of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $L^2$ metric structure of the Gaussian…
We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting…
In the stochastic network model of Britton and Lindholm [Dynamic random networks in dynamic populations. Journal of Statistical Physics, 2010], the number of individuals evolves according to a supercritical linear birth and death process,…