Related papers: Finite size corrections to the Parisi overlap func…
Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. A method is presented to correct for such errors. We show that MB FS effects can be effectively included in a…
In this work we analyze how effects of finite size may modify the thermodynamics of a system of strongly interacting fermions that we model using an effective field theory with four-point interactions at finite temperature and density and…
The scaling of the number of Rydberg excitations in a laser-driven cloud of atoms with the interaction strength is found to be affected by the finite size of the system. The scaling predicted by a theoretical model is compared with results…
Jamming criticality defines a universality class that includes systems as diverse as glasses, colloids, foams, amorphous solids, constraint satisfaction problems, neural networks, etc. A particularly interesting feature of this class is…
In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…
The effect of relative entropy asymmetry is analyzed in the context of empirical risk minimization (ERM) with relative entropy regularization (ERM-RER). Two regularizations are considered: $(a)$ the relative entropy of the measure to be…
Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement $\alpha$-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry like the…
According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation,…
We study (analytic) finite-size corrections in the dense polymer model on the strip by perturbing the critical Hamiltonian with irrelevant operators belonging to the tower of the identity. We generalize the perturbation expansion to include…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…
In this paper, we investigate the approximation properties of solutions to the Ginzburg-Landau equation (GLE) in finite element spaces. Special attention is given to how the errors are influenced by coupling the mesh size $h$ and the…
This thesis focus on the extension of the Parisi full replica symmetry breaking solution to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity…
An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…
Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, such as learning modular arithmetic…
We develop the finite-size scaling (FSS) theory at quantum transitions, considering generic boundary conditions, such as open and periodic boundary conditions, and also the corrections to the leading FSS behaviors. Using…
The thermodynamical cluster model is known to present a first-order liquid-gas phase transition in the idealized case of an uncharged, infinitely extended medium. However, in most practical applications of this model, the system is finite…
We study the phase transitions of a random copolymer chain with quenched disorder. We apply a replica variational approach based on a Gaussian trial Hamiltonian in terms of the correlation functions of monomer Fourier coordinates. This…
The continuous random energy model (CREM) is a toy model of spin glasses on $\{0,1\}^N$ that, in the limit, exhibits an infinitely hierarchical correlation structure. We give two polynomial-time algorithms to approximately sample from the…
A single McCulloch-Pitts neuron, that is, the simple perceptron is studied, with focus on the region beyond storage capacity. It is shown that Parisi's hierarchical ansatz for the overlap matrix of the synaptic couplings with so called…
The arithmetic mean/geometric mean-inequality (AM/GM-inequality) facilitates classes of non-negativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic…