Related papers: Finite size corrections to the Parisi overlap func…
We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random $N (\gg 1)$-dimensional Gaussian landscape and confined by a…
We calculate the corrections to the thermodynamic limit of the critical density for jamming in the Kob-Andersen and Fredrickson-Andersen kinetically-constrained models, and find them to be finite-density corrections, and not finite-size…
We consider a one-step replica symmetry breaking description of the Edwards-Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on…
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…
When fitting generalized linear mixed models (GLMMs), one important decision to make relates to the choice of the random effects distribution. As the random effects are unobserved, misspecification of this distribution is a real…
We study numerically finite-size corrections in scaling relations for roughness distributions of various interface growth models. The most common relation, which considers the average roughness $<w_2>$ as scaling factor, is not obeyed in…
In this work we discuss a short range version of the $p$-spin model. The model is provided with a parameter that allows to control the crossover with the mean field behaviour. We detect a discrepancy between the perturbative approach and…
Consider a correlated Gaussian random energy model built by successively adding one particle (spin) into the system and imposing the positivity of the associated covariance matrix. We show that the validity of a recently isolated condition…
The complete phase diagram of Random Energy Model (REM) is obtained for complex temperatures using the method proposed by Derrida. We find the density of zeroes for statistical sum. Then the method is applied to Generalized Random Energy…
The learning properties of finite size polynomial Support Vector Machines are analyzed in the case of realizable classification tasks. The normalization of the high order features acts as a squeezing factor, introducing a strong anisotropy…
We study the Replica Symmetric region of general multi-species Sherrington-Kirkpatrick (MSK) Model and answer some of the questions raised in Ann.~Probab.~43~(2015), no.~6, 3494--3513, where the author proved the Parisi formula under…
In this paper, we investigate the finite connectivity spin-glass problem. Our work is focused on the expansion around the point of infinite connectivity of the free energy of a spin glass on a graph with Poissonian distributed connectivity:…
The leading correction to the smoothed connected energy density-density correlation function is obtained for the large energy difference, within the context of the Gaussian Random Matrix Theory. In order to achieve this result, the…
We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica…
We consider the symmetry-resolved R\'{e}nyi and entanglement entropies for two-dimensional conformal field theories on a circle at nonzero temperature. We assume a unique ground state with a nonzero mass gap induced by the system's finite…
We propose a simpler approach to identifying the limit of free energy in a vector spin glass model by adding a self-overlap correction to the Hamiltonian. This avoids constraining the self-overlap and allows us to identify the limit with…
We study increasing subsequences (IS) for an ensemble of sequences given by permutation of numbers {1,2,...,n}. We consider a Boltzmann ensemble at temperature T. Thus each IS appears with the corresponding Boltzmann probability where the…
In this letter, we focus on the size effect of granular column collapses, which are potentially connected to the dynamics of complex geophysical flows, even if the link between microscopic structures of granular assemblies and their…
We study analytically the corrections to the leading terms in the Renyi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise…
Entropy integrals are widely used as a powerful empirical process tool to obtain upper bounds for the rates of convergence of global empirical risk minimizers (ERMs), in standard settings such as density estimation and regression. The upper…