Related papers: Generating Function for Particle-Number Probabilit…
Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…
We study the distribution of particle number in extended subsystems of a one-dimensional non-interacting Fermi gas confined in a potential well at zero temperature. Universal features are identified in the scaled bulk and edge regions of…
Motivated by recent real-time electron counting experiments, we evaluate the full counting statistics (FCS) for the probability distribution of the electron number inside a quantum dot which is weakly coupled to source and drain leads. A…
The critical behavior of the $(n+1)$-states Potts model in $d$-dimensions is studied with functional renormalization group techniques. We devise a general method to derive $\beta$-functions for continuos values of $d$ and $n$ and we write…
This paper introduces a new percolation model motivated from polymer materials. The mathematical model is defined over a random cubical set in the $d$-dimensional space $\mathbb{R}^d$ and focuses on generations and percolations of…
We study the problem of the computation of the effective diffusion constant of a Brownian particle diffusing in a random potential which is given by a function $V(\phi)$ of a Gaussian field $\phi$. A self similar renormalization group…
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary…
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical $(u,v)$ flower network. Using the renormalization-group like procedure, we derive the recursion relations for the percolating…
Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
The two parameter Poisson-Dirichlet distribution $PD(\alpha,\theta)$ is the distribution of an infinite dimensional random discrete probability. It is a generalization of Kingman's Poisson-Dirichlet distribution. The two parameter Dirichlet…
Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…
We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…
The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
We investigate Gaussian Universality for data distributions generated via diffusion models. By Gaussian Universality we mean that the test error of a generalized linear model $f(\mathbf{W})$ trained for a classification task on the…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…