Related papers: Fredholm determinants in the multiparticle hopping…
Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…
The diagonal spin-spin correlations of the square lattice Ising model, originally expressed as Toeplitz determinants, are given by two distinct Fredholm determinants - one with an integral operator having an Appell function kernel and…
We compute the full probability distribution of the positions of a tagged particle exactly for given arbitrary initial positions of the particles and for general single-particle propagators. We consider the thermodynamic limit of our exact…
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 investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…
We consider the parabolic Anderson model (PAM) which is given by the equation $\partial u/\partial t = \kappa\Delta u + \xi u$ with $u\colon\, \Z^d\times [0,\infty)\to \R$, where $\kappa \in [0,\infty)$ is the diffusion constant, $\Delta$…
Predicting counterfactual outcomes in longitudinal data, where sequential treatment decisions heavily depend on evolving patient states, is critical yet notoriously challenging due to complex time-dependent confounding and inadequate…
Statistical properties of the front of a semi-infinite system of single-file diffusion (one dimensional system where particles cannot pass each other, but in-between collisions each one independently follow diffusive motion) are…
This paper studies Markov Decision Processes (MDPs) with atomless initial state distributions and atomless transition probabilities. Such MDPs are called atomless. The initial state distribution is considered to be fixed. We show that for…
In this work we propose a two-dimensional extension of a previously defined one-dimensional version of a model of counterflowing particles, which considers an adapted Fermi-Dirac distribution to describe the transition probabilities. In…
We consider the PushTASEP (pushing totally asymmetric simple exclusion process, also sometimes called long-range TASEP) with the step initial configuration evolving in an inhomogeneous space. That is, the rate of each particle's jump…
Inter-relations between random matrix ensembles with different symmetry types provide inter-relations between generating functions for the gap probabilites at the spectrum edge. Combining these in the scaled limit with the exact evaluation…
We show that the transition probability of the Markoc chain $(G(j,1),...,G(j,n))_{j\ge 1}$, where the $G(i,j)'s$ are certain directed last-passage times, is given by a determinant of a special form. An analogous formula has recently been…
We present the conditional determinantal point process (DPP) approach to obtain new (mostly Fredholm determinantal) expressions for various eigenvalue statistics in random matrix theory. It is well-known that many (especially $\beta=2$)…
In this paper, we are concerned with a class of conservative systems including asymmetric exclusion processes and zero-range processes as examples, where some particles are initially placed on $N$ positions. A particle jumps from a position…
Using the Bethe ansatz we obtain in a determinant form the exact solution of the master equation for the conditional probabilities of the totally asymmetric exclusion process with particle-dependent hopping rates on Z. From this we derive a…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure…
We obtain "large gap" asymptotics for a Fredholm determinant with a confluent hypergeometric kernel. We also obtain asymptotics for determinants with two types of Bessel kernels which appeared in random matrix theory.
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
The explicit expression for the two time free energy distribution function in one-dimensional random directed polymers is derived in terms of the Bethe ansatz replica technique. It is show that such type of the distribution function can be…