Related papers: Formulas for Joint Probabilities for the Asymmetri…
We consider the simple exclusion process in the integer segment $ [1, N]$ with $k\le N/2$ particles and spatially inhomogenous jumping rates. A particle at site $x\in [ 1, N]$ jumps to site $x-1$ (if $x\ge 2$) at rate $1-\omega_x$ and to…
An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a…
We derive an explicit sum formula for symmetric Macdonald polynomials. Our expression contains multiple sums over the symmetric group and uses the action of Hecke generators on the ring of polynomials. In the special cases $t=1$ and $q=0$,…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
Many scientifically well-motivated statistical models in natural, engineering and environmental sciences are specified through a generative process, but in some cases it may not be possible to write down a likelihood for these models…
Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
In an earlier paper, we discussed the probability that the determinant of a matrix undergoes the least change upon perturbation of one of its elements, provided that most or all of the elements of the matrix are chosen at random and that…
Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the…
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative…
We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate $p\in(1/2,1]$ and to the left at rate $1-p$, interacting by exclusion. In the initial state there is a finite region…
The joint likelihood is a simple extension of the standard likelihood formalism that enables the estimation of common parameters across disjoint datasets. Joining the likelihood, rather than the data itself, means nuisance parameters can be…
Particle filters are applicable to a wide range of nonlinear, non-Gaussian state-space models and have already been applied to a variety of problems. However, there is a problem in the calculation of smoothed distributions, where particles…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
We are interested in random uniform minimal factorizations of the $n$-cycle which are factorizations of $(1~2\dots n)$ into a product of $n-1$ transpositions. Our main result is an explicit formula for the joint probability that 1 and 2…
This paper proposes a new method for estimating the joint probability mass function of a pair of discrete random variables. This estimator is used to construct joint Shannon R\'enyi-Tsallis entropies, and the mutual information estimates of…
We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible…
A formalism is presented to obtain closed evolution equations for asymptotic probability distribution functions of turbulence magnitudes. The formalism is derived for a generic evolution equation, so that the final result can be easily…
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…
We propose a simple, intuitive alternative method of deriving the rule for connecting asymptotic wave function amplitudes to scattering probabilities. This is illustrated using the standard example of a 1-D particle reflecting or…