Related papers: Generating Functions for Asymmetric Random Walk Pr…
We give a formula for the bivariate generating function of a stationary 1-dependent counting process in terms of its run probability generating function, with a probabilistic proof. The formula reduces to the well known bivariate generating…
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…
We consider walks on the edges of the square lattice $\mathbb Z^2$ which obey \emph{two-step rules,} which allow (or forbid) steps in a given direction to be followed by steps in another direction. We classify these rules according to a…
Let $G$ be a finitely generated group equipped with a finite symmetric generating set and the associated word length function $|\cdot |$. We study the behavior of the probability of return for random walks driven by symmetric measures $\mu$…
We consider a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…
We provide operadic interpretations for two Hopf subalgebras of the algebra of parking functions. The Catalan subalgebra is identified with the free duplicial algebra on one generator, and the Schr\"oder subalgebra is interpreted by means…
We refine necessary and sufficient conditions for the generating series of a weighted model of a quarter plane walk to be differentially algebraic. In addition, we give algorithms based on the theory of Mordell-Weil lattices, that, for each…
A lattice walk model is said to be reluctant if the defining step set has a strong drift towards the boundaries. We describe efficient random generation strategies for these walks.
We focus on the algebraic area probability distribution of planar random walks on a square lattice with $m_1$, $m_2$, $l_1$ and $l_2$ steps right, left, up and down. We aim, in particular, at the algebraic area generating function…
We provide formulas for generating functions of many types of paths in various rooted tree structures. We compute the $k$th moment of the generating functions for various types of vertical paths. In two specific familes of trees we find…
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 apply multivariate Lagrange interpolation to synthesize polynomial quantitative loop invariants for probabilistic programs. We reduce the computation of an quantitative loop invariant to solving constraints over program variables and…
We give sufficient conditions on the rates of two asymmetric exclusion processes such that the existence of a blocking invariant measure for the first implies the existence of such a measure for the second. The main tool is a coupling…
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…
Random multiplicative processes $w_t =\lambda_1 \lambda_2 ... \lambda_t$ (with < \lambda_j > 0 ) lead, in the presence of a boundary constraint, to a distribution $P(w_t)$ in the form of a power law $w_t^{-(1+\mu)}$. We provide a simple and…
We propose a novel stochastic method to exactly generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time $t_{f}$. These paths are weighted with a probability given by the overdamped…
In this paper, we first form a method to calculate the probability generating function of the total progeny of multitype branching process. As examples, we calculate probability generating function of the total progeny of the multitype…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
We give precise asymptotics to the number of first time returning random walks in the standard orthogonal lattice in $\mathbb{R}$ and we prove that these numbers do not form a $P$-recursive sequence. In the process, the known asymptotics of…
This work considers lattice walks restricted to the quarter plane, with steps taken from a set of cardinality three. We present a complete classification of the generating functions of these walks with respect to the classes algebraic,…