相关论文: Finite size correction to the spectrum of regular …

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with $N$ nodes and $N^{\gamma}$ edges, with $1 < \gamma \leq 2$. By conveniently rescaling the coupling constant, the free…

In this paper we study the diameter of the random graph $G(n,p)$, i.e., the the largest finite distance between two vertices, for a wide range of functions $p=p(n)$. For $p=\la/n$ with $\la>1$ constant, we give a simple proof of an…

We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution…

We compute and explore numerically the finite system size correction to NLO $2\to2$ scattering in massive scalar $\phi^4$ theory. The derivation uses "denominator regularization" (instead of the usual dimensional regularization) on a…

We present results from an ongoing project concerned with the computation of $\mathcal{O}(1/m_Q)$ and $\mathcal{O}(1/m_Q^2)$ relativistic corrections to the static potential. These corrections are extracted from Wilson loops with two…

Let $\mathcal A$ be the adjacency matrix of a random $d$-regular graph on $N$ vertices, and we denote its eigenvalues by $\lambda_1\geq \lambda_2\cdots \geq \lambda_{N}$. For $N^{2/3}\ll d\leq N/2$, we prove optimal rigidity estimates of…

We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…

We study the convergence and shape correction to the limit distributions of extreme values due to the finite size (FS) of data sets. A renormalization method is introduced for the case of independent, identically distributed (iid)…

We study existence and universality of scaling limits for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward's equation, which is an identity satisfied by the 1-point…

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…

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…

We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\frac{1}{n}\sum_{k=1}^n\exp\{-uG_{kk}(z)\}$ with $G(z)=(z-iA)^{-1}$. We prove that the moments of fluctuations normalized by…

The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…

We consider the normalized adjacency matrix of a random $d$-regular graph on $N$ vertices with any fixed degree $d\geq 3$ and denote its eigenvalues as $\lambda_1=d/\sqrt{d-1}\geq \lambda_2\geq\lambda_3\cdots\geq \lambda_N$. We establish…

Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known as highly relevant, in…

We consider the following random graph process: starting with n isolated vertices, add edges uniformly at random provided no such edge creates a copy of C_4. We show that, with probability tending to 1 as $n \to \infty$, the final graph…

The recent paper "Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices" by G.S. Dhesi and M. Ausloos [Phys. Rev. E 93 (2016), 062115] uses the replica method to compute the $1/N$ correction to…

In statistical mechanics, evaluating finite-size macroscopic fluctuations typically relies on Edgeworth expansions. However, these perturbative methods append additive polynomial corrections that inevitably break down in the large deviation…

Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to…

We consider a class of sparse random matrices which includes the adjacency matrix of the Erd\H{o}s-R\'enyi graph $\mathcal{G}(N,p)$. We show that if $N^{\varepsilon} \leq Np \leq N^{1/3-\varepsilon}$ then all nontrivial eigenvalues away…