Related papers: Watermelon configurations with wall interaction: e…
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 derive exact and asymptotic results for the number of star and watermelon configurations of vicious walkers confined to lie between two impenetrable walls, as well as for the analogous problem for $\infty$-friendly walkers. Our proofs…
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 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 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…
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…
A watermelon is a set of $p$ Bernoulli paths starting and ending at the same ordinate, that do not intersect. In this paper, we show the convergence in distribution of two sorts of watermelons (with or without wall condition) to processes…
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 generalize the classical work of de Bruijn, Knuth and Rice (giving the asymptotics of the average height of Dyck paths of length $n$) to the case of $p$--watermelons with a wall (i.e., to a certain family of $p$ nonintersecting Dyck…
The exact solution of directed self-avoiding walks confined to a slit of finite width and interacting with the walls of the slit via an attractive potential has been calculated recently. The walks can be considered to model the…
Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of…
We investigate a model of continuous-time simple random walk paths in $\mathbb{Z}^d$ undergoing two competing interactions: an attractive one towards the large values of a random potential, and a self-repellent one in the spirit of the…
We consider a family of linearly elastic shells with thickness $2\varepsilon$ (where $\varepsilon$ is a small parameter). The shells are clamped along a portion of their lateral face, all having the same middle surface $S$, and may enter in…
We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry natural notions of subadditivity, allowing the effective study…
We find and analyse the exact solution of a model of three different polymers with asymmetric contact interactions in two dimensions, modelling a scenario where there are different types of polymers involved. In particular, we find the…
We consider a two-body quantum system in dimension one composed by a test particle interacting with an harmonic oscillator placed at the position $a>0$. At time zero the test particle is concentrated around the position $R_0$ with average…
We study the watermelon probabilities in the uniform spanning forests on the two-dimensional semi-infinite square lattice near either open or closed boundary to which the forests can or cannot be rooted, respectively. We derive universal…
We derive asymptotics for the moments as well as the weak limit of the height distribution of watermelons with p branches with wall. This generalises a famous result of de Bruijn, Knuth and Rice on the average height of planted plane trees,…
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 study the wetting model, which considers a random walk constrained to remain above a hard wall, but with additional pinning potential for each contact with the wall. This model is known to exhibit a wetting phase transition, from a…