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Related papers: Finite size corrections to the Parisi overlap func…

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We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…

Statistical Mechanics · Physics 2026-03-02 Yucheng Liu , Jiwoon Park , Gordon Slade

We study a generalization of the model introduced by Kistler and Schmidt in $2015$, that interpolates between the random energy model (REM) and the branching random walk (BRW). More precisely, we are interested in the asymptotic behaviour…

Probability · Mathematics 2021-12-21 Mohamed Ali Belloum

Phylogenomics, even more so than traditional phylogenetics, needs to represent the uncertainty in evolutionary trees due to systematic error. Here we illustrate the analysis of genome-scale alignments of yeast, using robust measures of the…

Populations and Evolution · Quantitative Biology 2009-12-31 Peter J. Waddell , Ariful Azad

We introduce and study a class of particle hopping models consisting of a single box coupled to a pair of reservoirs. Despite being zero-dimensional, in the limit of large particle number and long observation time, the current and activity…

Statistical Mechanics · Physics 2022-08-31 Yongjoo Baek , Yariv Kafri , Vivien Lecomte

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…

We get back to the computation of the leading finite size corrections to some random link matching problems, first adressed by Mezard and Parisi [J. Physique 48 (1987) 1451-1459]. In the so-called bipartite case, their result is in…

Disordered Systems and Neural Networks · Physics 2009-11-07 G. Parisi , M. Ratieville

Resetting is a renewal mechanism in which a process is intermittently repeated after a random or fixed time. This simple act of stop and repeat profoundly influences the behaviour of a system as exemplified by the emergence of…

Statistical Mechanics · Physics 2024-03-22 Saikat Santra , Prashant Singh

We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap $R^{1,2}$…

Mathematical Physics · Physics 2024-02-27 Chigak Itoi , Hisamitsu Mukaida , Hal Tasaki

We report on the exact treatment of a random-matrix representation of bond percolation model on a square lattice in two dimensions with occupation probability $p$. The percolation problem is mapped onto a random complex matrix composed of…

Statistical Mechanics · Physics 2022-02-14 Azadeh Malekan , Sina Saber , Abbas Ali Saberi

In this paper we study finite interaction range corrections to the mosaic picture of the glass transition as emerges from the study of the Kac limit of large interaction range for disordered models. To this aim we consider point to set…

Disordered Systems and Neural Networks · Physics 2009-11-13 Silvio Franz , Giorgio Parisi , Federico Ricci-Tersenghi

By finding local minima of an enthalpy-like energy, we can generate jammed packings of frictionless spheres under constant shear stress $\sigma$ and obtain the yield stress $\sigma_y$ by sampling the potential energy landscape. For…

Soft Condensed Matter · Physics 2014-06-09 Hao Liu , Xiaoyi Xie , Ning Xu

We analyze the prediction error of ridge regression in an asymptotic regime where the sample size and dimension go to infinity at a proportional rate. In particular, we consider the role played by the structure of the true regression…

Statistics Theory · Mathematics 2021-03-09 Dominic Richards , Jaouad Mourtada , Lorenzo Rosasco

We study the spin glass system consisting of a Random Energy Model coupled with a random magnetic field. This system was investigated by de Oliveira Filho, da Costa and Yokoi (Phys. Rev. E 74 [2006]) who computed the free energy. In this…

Probability · Mathematics 2015-06-18 Louis-Pierre Arguin , Nicola Kistler

A popular current research trend deals with expanding the Monte-Carlo tree search sampling methodologies to the environments with uncertainty and incomplete information. Recently a finite population version of Geiringer theorem with…

Artificial Intelligence · Computer Science 2013-05-14 Boris Mitavskiy , Jun He

The analogue of the paramagnetic to spin-glass phase transition in disordered magnetic systems, leading to the phenomenon of replica symmetry breaking, has been recently demonstrated in a two-dimensional random laser consisting of an…

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

Machine Learning · Statistics 2017-11-07 Jason Xu , Eric C. Chi , Kenneth Lange

We introduce an effective field theory approach that describes the motion of finite size objects under the influence of electromagnetic fields. We prove that leading order effects due to the finite radius $R$ of a spherically symmetric…

General Relativity and Quantum Cosmology · Physics 2013-05-29 Chad R. Galley , Adam K. Leibovich , Ira Z. Rothstein

We introduce a straightforward Gaussian process regression (GPR) model for the transition structure factor of metal periodic coupled cluster singles and doubles (CCSD) calculations. This is inspired by the method introduced by Liao and…

Computational Physics · Physics 2022-06-08 Laura Weiler , Tina N. Mihm , James J. Shepherd

We investigate finite-size effects on the chiral phase diagram of strong interactions within the linear sigma model coupled to quarks. We estimate the modification of the pseudocritical transition line and isentropic trajectories for sizes…

Nuclear Theory · Physics 2011-07-14 L. F. Palhares , E. S. Fraga , T. Kodama

We study a heteropolymer model with random contact interactions introduced some time ago as a simplified model for proteins. The model consists of self-avoiding walks on the simple cubic lattice, with contact interactions between nearest…

Soft Condensed Matter · Physics 2009-10-31 Ugo Bastolla , Peter Grassberger