相关论文: Logarithmic corrections to gap scaling in random-b…
We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same…
We establish large deviation type estimates for i.i.d. products of two dimensional random matrices with finitely supported probability distribution. The estimates are stable under perturbations and require no irreducibility assumptions. In…
The problem of developing an adaptive isogeometric method (AIGM) for solving elliptic second-order partial differential equations with truncated hierarchical B-splines of arbitrary degree and different order of continuity is addressed. The…
In this paper the local iterative Lie-Schwinger block-diagonalization method, introduced in [FP], [DFPR1], and [DFPR2] for quantum chains, is extended to higher-dimensional quantum lattice systems with Hamiltonians that can be written as…
We demonstrate that the integrality gap of the natural cut-based LP relaxation for the directed Steiner tree problem is $O(\log k)$ in quasi-bipartite graphs with $k$ terminals. Such instances can be seen to generalize set cover, so the…
We consider a magnetic Schroedinger operator in a planar infinite strip with frequently and non-periodically alternating Dirichlet and Robin boundary conditions. Assuming that the homogenized boundary condition is the Dirichlet or the Robin…
We consider the problem of learning the underlying graph of a sparse Ising model with $p$ nodes from $n$ i.i.d. samples. The most recent and best performing approaches combine an empirical loss (the logistic regression loss or the…
Consider the Hill operator $Ty=-y''+q'(t)y$ in $L^2(\R)$, where $q\in L^2(0,1)$ is a 1-periodic real potential. The spectrum of $T$ is is absolutely continuous and consists of bands separated by gaps $\g_n,n\ge 1$ with length $|\g_n|\ge 0$.…
Random bond Ising systems on a general hierarchical lattice are considered. Interesting inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These lead to upper bounds on the…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…
In this short note we describe a simple but remarkably effective method for rigorously estimating Lyapunov exponents for expanding maps of the interval. We illustrate the applicability of this method with some standard examples.
Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…
The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the…
These notes are a supplementary file to the paper Hopf bifurcations for HANDY-type models (M. Badiale and I. Cravero, under submission), providing full details of the computations developed in Section 4.2. The purpose of this supplement is…
We consider normalized Laplacians and their perturbations by periodic potentials (Schr\"odinger operators) on periodic discrete graphs. The spectrum of the operators consists of an absolutely continuous part (a union of a finite number of…
Given a negatively curved compact Riemannian surface $X$, we give an explicit estimate, valid with high probability as the degree goes to infinity, of the first non-trivial eigenvalue of the Laplacian on random Riemannian covers of $X$. The…
We propose new methods for calculation of the discrete spectrum, the reflection amplitude and the correlation functions of boundary Liouville theory on a strip with Lorentzian signature. They are based on the structure of the vertex…
Band engineering in twisted bilayers of the five generic two-dimensional Bravais networks is demonstrated. We first derive symmetry-based constraints on the interlayer coupling, which helps us to predict and understand the shape of the…
We develop a controlled diagrammatic framework for periodic Anderson models,and apply it to heterostrained magic-angle twisted bilayer graphene (MATBG) at charge neutrality using the topological heavy-fermion formulation. Building on…
Sampling Gibbs measures at low temperatures is an important task but computationally challenging. Numerical evidence suggests that the infinite-swapping algorithm (isa) is a promising method. The isa can be seen as an improvement of the…