相关论文: One step beyond: The excursion set approach with c…
The excursion set theory of halo formation is modified by adopting the fractional Brownian motion, to account for possible correlation between merging steps. We worked out analytically the conditional mass function, halo merging rate and…
This work is to popularize the method of computing the distribution of the excursion times for a Gaussian process that involves extended and multivariate Rice's formula. The approach was used in numerical implementations of the…
We propose a method of estimating the uncertainty of a result obtained through extrapolation to the complete basis set limit. The method is based on an ensemble of random walks which simulate all possible extrapolation outcomes that could…
The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…
We study the halo-matter cross bispectrum in the presence of primordial non-Gaussianity of the local type. We restrict ourselves to the squeezed limit, for which the calculation are straightforward, and perform the measurements in the…
We investigate nonlocal Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We begin by writing down a bias expansion which includes all the…
We present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…
We consider a random walk in confined geometry, starting from a site and eventually reaching a target site. We calculate analytically the distribution of the occupation time on a third site, before reaching the target site. The obtained…
We use the concept of excursions for the prediction of random variables without any moment existence assumptions. To do so, an excursion metric on the space of random variables is defined which appears to be a kind of a weighted…
We study first-passage statistics for one-dimensional random walks $S_n$ with independent and identically distributed jumps starting from the origin. We focus on the joint distribution of the first-passage time $\tau_b$ and first-passage…
In the ellipsoidal collapse model, the critical density for the collapse of a gravitationally bound object is a function of its mass. In the excursion set formalism, this translates into a moving barrier problem such that the mass function…
Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e.…
We develop a new, simple, fast and parameter-free method to construct dark matter halo catalogues. This method requires as inputs only the linear matter power spectrum and the threshold density for halo formation in linear theory. It…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
We consider a one dimensional random-walk-like process, whose steps are centered Gaussians with variances which are determined according to the sequence of arrivals of a Poisson process on the line. This process is decorated by independent…
Excursion set theory (EST) is an analytical framework to study the large-scale structure of the Universe. EST introduces a procedure to calculate the number density of structures by relating the cosmological linear perturbation theory to…