相关论文: Vicious walkers, friendly walkers and Young tablea…

We derive new results for the number of star and watermelon configurations of vicious walkers in the presence of an impenetrable wall by showing that these follow from standard results in the theory of Young tableaux, and combinatorial…

We perform an exact and asymptotic analysis of the model of $n$ vicious walkers interacting with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More specifically, we study the partition function of watermelon…

We find, and analyse, the exact solution of two friendly directed walks, modelling polymers, which interact with a wall via contact interactions. We specifically consider two walks that begin and end together so as to imitate a polygon. We…

We consider N vicious walkers moving in one dimension in a one-body potential v(x). Using the backward Fokker-Planck equation we derive exact results for the asymptotic form of the survival probability Q(x,t) of vicious walkers initially…

A vicious walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to…

A one-dimensional system of nonintersecting Brownian particles is constructed as the diffusion scaling limit of Fisher's vicious random walk model. $N$ Brownian particles start from the origin at time $t=0$ and undergo mutually avoiding…

We establish a reflection principle for three lattice walkers and use this principle to reduce the enumeration of the configurations of three vicious walkers to that of configurations of two vicious walkers. In the combinatorial treatment…

The vicious random walker problem on a one dimensional lattice is considered. Many walkers take simultaneous steps on the lattice and the configurations in which two of them arrive at the same site are prohibited. It is known that the…

Asymptotic results are derived for the number of random walks in alcoves of affine Weyl groups (which are certain regions in $n$-dimensional Euclidean space bounded by hyperplanes), thus solving problems posed by Grabiner [J. Combin. Theory…

We consider a statistical system in a planar wedge, for values of the bulk parameters corresponding to a first order phase transition and with boundary conditions inducing phase separation. Our previous exact field theoretical solution for…

We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker's…

We study the extreme statistics of N non-intersecting Brownian motions (vicious walkers) over a unit time interval in one dimension. Using path-integral techniques we compute exactly the joint distribution of the maximum M and of the time…

A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version…

We consider lattice walks in $\R^k$ confined to the region $0<x_1<x_2...<x_k$ with fixed (but arbitrary) starting and end points. The walks are required to be "reflectable", that is, we assume that the number of paths can be counted using…

We consider a generalisation of the vicious walker problem in which N random walkers in R^d are grouped into p families. Using field-theoretic renormalisation group methods we calculate the asymptotic behaviour of the probability that no…

We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in…

We investigate the asymptotic behaviour of a class of self-interacting nearest neighbour random walks on the one-dimensional integer lattice which are pushed by a particular linear combination of their own local time on edges in the…

The existence and multiplicity of similarity solutions for the steady, incompressible and fully developed laminar flows in a uniformly porous channel with two permeable walls are investigated. We shall focus on the so-called asymmetric case…

Using path integral techniques, we compute exactly the distribution of the maximal height H_p of p nonintersecting Brownian walkers over a unit time interval in one dimension, both for excursions (p-watermelons with a wall) and bridges…

We determine the weak limit of the distribution of the random variables "height" and "range" on the set of p-watermelons without wall restriction as the number of steps tends to infinity. Additionally, we provide asymptotics for the moments…