Related papers: Determinant Calculations with Random Walk Worldlin…

We consider two dimensional random walks conditioned to stay in the positive quadrant. Assuming that the increments of the walk have finite second moments and that the drift vector is co-oriented with one of two axes, we construct positive…

We estimate the effects of dynamical fermions by extrapolating to positive flavour numbers the results from negative values obtained by adding to the pure gauge sector a fermion action where the fields obey a Bose statistics: the bermions.

Feller's book An Introduction to Probability Theory and Its Application discusses statistics corresponding to sequences of coin tosses, with a dollar being won or lost depending on the outcome of each toss. This is equivalent to analyzing…

In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential…

In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…

In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…

We propose and study an improved method to calculate the fermionic determinant of dynamical configurations. The evaluation or at least stochastic estimation of ratios of fermionic determinants is essential for a recently proposed updating…

We calculate explicit speeds for random walks in uniform degenerate random environments. For certain non-uniform random environments, we calculate speeds that are non-monotone.

We propose a strategy for conducting lattice QCD simulations at fixed volume but variable quark mass so as to investigate the physical effects of dynamical fermions. We present details of techniques which enable this to be carried out…

Considering as an example a simple lattice ansatz for the chiral fermion determinant, we demonstrate that even very mild violation of gauge invariance by the determinant at finite lattice spacing leads to the need for another scale in the…

We argue that lattice simulations of full QCD with varying quark mass are best conducted at fixed lattice spacing rather than at fixed $\beta$. We present techniques which enable this to be carried out effectively, namely the tuning in bare…

Quantum random walks, - coined, lattice ones, - exhibit ballistic behavior with fascinating asymptotic patterns of the amplitudes. We show that averaging over the coins (using the Haar measure), these patterns blend into a spline. Also, we…

We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…

Worldline representations were established as a powerful tool for studying bosonic lattice field theories at finite density. For fermions, however, the worldlines still may carry signs that originate from the Dirac algebra and from the…

The electromagnetic form factors provide important insight into the internal structure of the nucleon and continue to be of major interest for experiment and phenomenology. For an intermediate range of momenta the form factors can be…

A comprehensive number of integrals emerging in one-loop computations in a gauge perturbation theory on the lattice with Wilson fermions at $r=1$ is computed using the Burgio--Caracciolo--Pelissetto algorithm and the FORM package. An…

We calculate the third coefficient of the lattice beta function in QCD with Wilson fermions, extending the pure gauge results of Luescher and Weisz; we show how this coefficient modifies the scaling function on the lattice. We also…

We consider the motion of a particle on a Galton Watson tree, when the probabilities of jumping from a vertex to any one of its neighbours is determined by a random process. Given the tree, positive weights are assigned to the edges in such…

Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool for analyzing these walks; we provide a Maple package for…

Using the world-line method we resum the scalar one-loop effective action. This is based on an exact expression for the one-loop action obtained for a background potential and a Taylor expansion of the potential up to quadratic order in…