相关论文: Multiclass processes, dual points and M/M/1 queues
We prove a strong law of large numbers for the location of the second class particle in a totally asymmetric exclusion process when the process is started initially from a decreasing shock. This completes a study initiated in Ferrari and…
The intersection of numerical analysis and machine learning, particularly in the domain of Neural ODEs and Physics-Informed Neural Networks (PINNs), relies heavily on discrete approximations of continuous flows. However, in stiff systems,…
We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…
In the multi-type totally asymmetric simple exclusion process (TASEP) on the line, each site of Z is occupied by a particle labeled with some number, and two neighboring particles are interchanged at rate one if their labels are in…
Product matrix processes are multi-level point processes formed by the singular values of random matrix products. In this paper we study such processes where the products of up to $m$ complex random matrices are no longer independent, by…
We describe the translation invariant stationary states of the one dimensional discrete-time facilitated totally asymmetric simple exclusion process (F-TASEP). In this system a particle at site $j$ in $Z$ jumps, at integer times, to site…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary…
In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…
We consider simple random walks on random graphs embedded in $\mathbb{R}^d$ and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we…
Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested…
In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the…
Measure-valued Markov chains have raised interest in Bayesian nonparametrics since the seminal paper by (Math. Proc. Cambridge Philos. Soc. 105 (1989) 579--585) where a Markov chain having the law of the Dirichlet process as unique…
While run-and-tumble particles are a foundational model for self-propelled particles as bacteria or Janus particles, the analytical derivation of their steady state from the microscopic details is still an open problem. By directly modeling…
The boundary-induced phase transitions in an asymmetric simple exclusion process with inter-particle repulsion and bulk non-conservation are analyzed through the fixed points of the boundary layers. This system is known to have phases in…
We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP). Expectations of the duality functionals correspond…
We introduce an $n$-species totally asymmetric zero range process ($n$-TAZRP) on one-dimensional periodic lattice with $L$ sites. It is a continuous time Markov process in which $n$ species of particles hop to the adjacent site only in one…
We develop a bifurcation theory for infinite dimensional systems satisfying abstract hypotheses that are tailored for applications to mean field coupled chaotic maps. Our abstract theory can be applied to many cases, from globally coupled…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of…