Related papers: Generating Function for Particle-Number Probabilit…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
Nucleation and growth is studied in a system undergoing diffusion-controlled condensation under gradual changes in parameters, such as cooling. It is demonstrated that when Gibbs-Thompson effect becomes negligible, the system falls into a…
Diffusion models are distinguished by their exceptional generative performance, particularly in producing high-quality samples through iterative denoising. While current theory suggests that the number of denoising steps required for…
Both observational and theoretical research over the past decade has demonstrated that the probability distribution function (PDF) of the gas density in turbulent molecular clouds is a key ingredient for understanding star formation. It has…
Generalized parton distribution functions (GPDs) of spin-3/2 particles are defined for the first time in this paper. Eight unpolarized and eight polarized GPDs are found. In the forward limit of GPDs, the structure functions and parton…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
We study explosive percolation (EP) on Erd\"{o}s-R\'{e}nyi network for product rule (PR) and sum rule (SR). Initially, it was claimed that EP describes discontinuous phase transition, now it is well-accepted as a probabilistic model for…
Critical finite-size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions, the universal part of the…
Multiplicity distributions $P(N)$ measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies become more…
A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…
There exists an entire family of universal PDFs of the magnetization mode of the three dimensional Ising model parameterized by $\zeta = \lim_{L,\xi_{\infty}}L/\xi_{\infty}$ which is the ratio of the system size $L$ to the bulk correlation…
Recent work on percolation in $d=2$ [J. Phys. A {\bf 55} 204002] introduced an operator that gives a weight $k^{\ell}$ to configurations with $\ell$ `nested paths' (NP), i.e. disjoint cycles surrounding the origin, if there exists a cluster…
We analytically compute the full counting statistics of charge transfer in a classical automaton of interacting charged particles. Deriving a closed-form expression for the moment generating function with respect to a stationary equilibrium…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
This paper presents a study of power series distributions (PSD) with prescribed covariance characteristics. Such distributions constitute a fundamental class in probability theory and mathematical statistics, as they generalize a wide range…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
We propose a parametrization for the generalized parton distributions (GPDs) which is based on representation of parton distributions as an infinite series of t-channel exchanges. The entire generalized parton distribution is given as an…
The universal behaviour of the directed percolation universality class is well understood, both the critical scaling as well as finite size scaling. This article focuses on the block (finite size) scaling of the order parameter and its…
The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class,…
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent…