相关论文: Landscape approximation of the ground state eigenv…

We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the ground state approximation, as well as for the associated…

We consider the problem of sampling from the Ising model when the underlying interaction matrix has eigenvalues lying within an interval of length $\gamma$. Recent work in this setting has shown various algorithmic results that apply…

Motivated by its relevance to various types of dynamical behavior of network systems, the maximum eigenvalue $\lambda_Q$ of the adjacency matrix $A$ of a network has been considered, and mean-field-type approximations to $\lambda_Q$ have…

We prove spectral localization for infinite metric graphs with a self-adjoint Laplace operator and a random potential. To do so we adapt the multiscale analysis (MSA) from the R^d-case to metric graphs. In the MSA a covering of the graph is…

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…

It is known that, for an oriented hypergraph with (vertex) coloring number $\chi$ and smallest and largest normalized Laplacian eigenvalues $\lambda_1$ and $\lambda_N$, respectively, the inequality $\chi\geq…

In this paper we are concerned with the approximation of functions by single hidden layer neural networks with ReLU activation functions on the unit circle. In particular, we are interested in the case when the number of data-points exceeds…

A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…

In this work, we study some statistical properties of the extreme eigenstates of the randomly-weighted adjacency matrices of random graphs. We focus on two random graph models: Erd\H{o}s-R\'{e}nyi (ER) graphs and random geometric graphs…

We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically…

We prove a transfer theorem for hereditary classes of $(r+1)$-uniform hypergraphs. Let $\mathcal H$ be such a class, and for $H\in\mathcal H$ write $\Delta(H)$ and $d(H)$ for the maximum degree and average degree of $H$, respectively. We…

We report a ground-state solution for the two-dimensional fermionic Hubbard model, which is obtained via a numerical variational method. The two ingredients in this approach are tensor network states and the time-evolving block decimation.…

We consider the 2D Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state…

We present a new method for upper bounding the second eigenvalue of the Laplacian of graphs. Our approach uses multi-commodity flows to deform the geometry of the graph; we embed the resulting metric into Euclidean space to recover a bound…

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…

The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…

We consider an elastic manifold of internal dimension $d$ and length $L$ pinned in a $N$ dimensional random potential and confined by an additional parabolic potential of curvature $\mu$. We are interested in the mean spectral density…

This paper concerns spectral properties of linear Schr\"odinger operators under oscillatory high-amplitude potentials on bounded domains. Depending on the degree of disorder, we prove the existence of spectral gaps amongst the lowermost…

Let $G=(V,E)$ be a $d$-regular graph on $n$ vertices and let $\mu_0$ be a probability measure on $V$. The act of moving to a randomly chosen neighbor leads to a sequence of probability measures supported on $V$ given by $\mu_{k+1} = A…

A random $n$-lift of a base graph $G$ is its cover graph $H$ on the vertices $[n]\times V(G)$, where for each edge $u v$ in $G$ there is an independent uniform bijection $\pi$, and $H$ has all edges of the form $(i,u),(\pi(i),v)$. A main…