Related papers: The linear Ising model and its analytic continuati…
We consider random walk among iid, uniformly elliptic conductances on $\mathbb Z^d$, and prove the Einstein relation (see Theorem 1). It says that the derivative of the velocity of a biased walk as a function of the bias equals the…
Two principles explain emergence. First, in the Receipt's reference frame, Deg(S) = 4/3 Deg(R), where Supply S is an isotropic radiative energy source, Receipt R receives S's energy, and Deg is a system's degrees of freedom based on its…
The dynamics based on information transfer is proposed as an underlying mechanism for the scale-invariant dynamic critical behavior observed in a variety of systems. We apply the dynamics to the globally-coupled Ising model, which is…
A one-dimensional Ising model with nearest neighbour interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the…
This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained --…
Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally tree-like graph and factor…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…
An analysis is made of various methods of phenomenological renormalization based on finite-size scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made…
In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…
The complete framework for the $\epsilon$-machine construction of the one dimensional Ising model is presented correcting previous mistakes on the subject. The approach follows the known treatment of the Ising model as a Markov random…
The main contribution of the current study is two-fold. First, we investigate the energy landscape of the Ising and Potts models on finite two-dimensional lattices without external fields in the low temperature regime. The complete analysis…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…
Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually…
It is recognised now that a variety of real-life phenomena ranging from diffuson of cold atoms to motion of humans exhibit dispersal faster than normal diffusion. L\'evy walks is a model that excelled in describing such superdiffusive…
Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic…
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…