相关论文: Maximum and entropic repulsion for a Gaussian memb…
In this article we study the scaling limit of the interface model on $\mathbb{Z}^d$ where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free…
The assumption that the elements of the cost matrix in the classical assignment problem are drawn independently from a standard Gaussian distribution motivates the study of a particular Gaussian field indexed by the symmetric permutation…
We consider Kaplan's domain wall fermions in the presence of an Anti-de Sitter (AdS) background in the extra dimension. Just as in the flat space case, in a completely vector-like gauge theory defined after discretizing this extra…
We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally…
We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of $2$-modular lattices -- such as the $16$-dimensional Barnes-Wall lattice -- and $3$-modular lattices -- such as the $12$-dimensional…
We derive an asymptotic expansion for the critical percolation density of the random connection model as the dimension of the encapsulating space tends to infinity. We calculate rigorously the first expansion terms for the Gilbert disk…
We study the physics of a single discrete gravitational extra dimension using the effective field theory for massive gravitons. We first consider a minimal discretization with 4D gravitons on the sites and nearest neighbor hopping terms. At…
The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean…
We propose a quantum theory of membranes designed such that the ground-state wavefunction of the membrane with compact spatial topology \Sigma_h reproduces the partition function of the bosonic string on worldsheet \Sigma_h. The…
This is the first in a series of two works which study the discrete Gaussian free field on the binary tree when all leaves are conditioned to be positive. In this work, we obtain sharp asymptotics for the probability of this "hard-wall…
In-medium field-theory is applied to different effective models and QCD to describe mass and isospin effects, finite volume corrections and magnetic fields in the phase diagram of Strong Interactions, keeping close contact with experiments…
We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite dimensional spin glasses, and we analyze in detail the four dimensional Edwards-Anderson model with Gaussian…
Counterion distributions at charged soft membranes are studied using perturbative analytical and simulation methods in both weak coupling (mean-field or Poisson-Boltzmann) and strong coupling limits. The softer the membrane, the more…
In the study of quantum vacuum energy and the Casimir effect, it is desirable to model the conductor by a potential of the form $V(z)=z^\alpha$. This "soft wall" model was proposed so as to avoid the violation of the principle of virtual…
An analytically solvable cell fluid model with unrestricted cell occupancy, infinite-range Curie-Weiss-type attraction and short-range intra-cell repulsion is studied within the grand-canonical ensemble. Building on an exact single-integral…
The matrix model with a Bethe-tree embedding space (coinciding at large $N$ with the Kazakov-Migdal ``induced QCD'' model \cite{KM}) is investigated. We further elaborate the Riemann-Hilbert approach of \rf{Mig1} assuming certain…
The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As…
We consider a class of Gaussian Free Fields denoted by $(g_x)_{x \in {\cal V}_N}$, where $ {\cal V}_N = \{0,1\}^N$ and $N\in \mathbb{Z}_+$. These fields are related to a general class of $N$-dimensional random walks on the hypercube, which…
Logarithmic finite-size scaling of the O($n$) universality class at the upper critical dimensionality ($d_c=4$) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems.…
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through…