Related papers: A stronger topology for the Brownian web
We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…
In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear…
The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This…
We give tightness criteria for random variables taking values in the space of all compact sets of cadlag real-valued paths, in terms of both the Skorohod J1 and M1 topologies. This extends earlier work motivated by the study of the Brownian…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
Previously, Sarkar and Sun have shown that for supercritical oriented percolation in dimension $1+1$, the set of rightmost infinite open paths converges to the Brownian web after proper centering and scaling. In this note, we show that a…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space…
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…
This paper is concerned with the problem of defining and estimating statistics for distributions on spaces such as Riemannian manifolds and more general metric spaces. The challenge comes, in part, from the fact that statistics such as…
We consider the use of random walks as an approach to obtain connection coefficients for higher-order Bernoulli and Euler polynomials. In particular, we consider the cases of a $1$-dimensional linear reflected Brownian motion and of a…
The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph.…
We consider a variant of the radial spanning tree introduced by Baccelli and Bordenave. Like the original model, our model is a tree rooted at the origin, built on the realization of a planar Poisson point process. Unlike it, the paths of…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
We present continuum models that describe the evolution of the position of a random walker on a growing network using four different growth algorithms. Three of these involve a random element, including one in which the motility rate of the…
We explore some of the connections between the local picture left by the trace of simple random walk on a discrete cylinder with base a d-dimensional torus, d at least 2, of side-length N running for times of order N^{2d} and the model of…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely,…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…