相关论文: One step beyond: The excursion set approach with c…

One of the main predictions of excursion set theory is that the clustering of dark matter haloes only depends on halo mass. However, it has been long established that the clustering of haloes also depends on other properties, including…

We study cell count moments up to fifth order of the distributions of haloes, of halo substructures as a proxy for galaxies, and of mass in the context of the halo model and compare theoretical predictions to the results of numerical…

Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control…

The Press-Schechter (PS) and excursion set (ES) models of structure formation fail in reproducing the halo bias found in simulations, while the excursion set-peaks (ESP) formalism built in the peak model reproduces it only at high masses…

We study the entropy of the distribution of the set R_n of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of R_n if the graph…

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this…

We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian…

We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches…

Grazing transits present a special problem for statistical studies of exoplanets. Even though grazing planetary orbits are rare (due to geometric selection effects), for many low to moderate signal-to-noise cases, a significant fraction of…

We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing crossing paths and exibiting dependence before coalescence. We show that under diffusive scaling this system converges in distribution…

We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in Angel and Ray [3]. We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to…

In this article we compare the halo mass function predicted by the excursion set theory with a drifting diffusive barrier against the results of N-body simulations for several cosmological models. This includes the standard LCDM case for a…

Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…

We study the evolution of initially extended distributions in the coined quantum walk on the line by analyzing the dispersion relation of the process and its associated wave equations. This allows us, in particular, to devise an initially…

This paper uses numerical simulations to test the formation time distribution of dark matter haloes predicted by the analytic excursion set approaches. The formation time distribution is closely linked to the conditional mass function and…

We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass tracer scaling with mass are…

We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [-a,a]. For a of the order of one, the exit probabilities to each edge of the…

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes.…

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For…

We give exact and explicit expressions of mean first-passage times for random walks in a rectangular domain, in both cases of reflecting boundary conditions and periodic boundary conditions. The situations with one or two absorbing targets…