Related papers: Graphical constructions of simple exclusion proces…
The multispecies asymmetric simple exclusion process (mASEP) is a Markov chain in which particles of different species hop along a one-dimensional lattice. This paper studies the doubly asymmetric simple exclusion process…
We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy…
In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and explanations are provided as to how they apply to…
Duality relations for simple exclusion processes with general open boundaries are discussed. It is shown that a combination of spin operators and bosonic operators enables us to have an unified discussion for the duality relations with the…
We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses.…
We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that…
We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process.…
Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is…
Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…
Generating images from a single sample, as a newly developing branch of image synthesis, has attracted extensive attention. In this paper, we formulate this problem as sampling from the conditional distribution of a single image, and…
Recently, learned image compression has attracted considerable attention due to its superior performance over traditional methods. However, most existing approaches employ a single entropy model to estimate the probability distribution of…
We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological…
Graph embedding generation techniques aim to learn low-dimensional vectors for each node in a graph and have recently gained increasing research attention. Publishing low-dimensional node vectors enables various graph analysis tasks, such…
The Fiedler vector of a graph, namely the eigenvector corresponding to the second smallest eigenvalue of a graph Laplacian matrix, plays an important role in spectral graph theory with applications in problems such as graph bi-partitioning…
Understanding the data-generating process is essential for building machine learning models that generalise well while ensuring robustness and interpretability. This paper addresses the fundamental challenge of modelling the data generation…
The gap probability generating function has as its coefficients the probability of an interval containing exactly $k$ eigenvalues. For scaled random matrices with orthogonal symmetry, and the interval at the hard or soft spectrum edge, the…
We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space $\mathbb{X}$ equipped with a continuous function $f: \mathbb{X} \rightarrow \mathbb{R}$. We first give a categorification of the…
Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We consider an agent-based saturated open-city variant, the Flip Schelling Process (FSP), in which agents,…
In this paper, we introduce a sketching algorithm for constructing a tensor train representation of a probability density from its samples. Our method deviates from the standard recursive SVD-based procedure for constructing a tensor train.…
We construct a novel preorder on the set of nodes of a simple undirected graph. We prove that the preorder (induced by the topology of the graph) is preserved, e.g., by the logistic dynamical system (both in discrete and continuous time).…