Related papers: Excursion Set Theory for generic moving barriers a…
Random field excursions is an increasingly vital topic within data analysis in medicine, cosmology, materials science, etc. This work is the first detailed study of their Betti numbers in the so-called `sparse' regime. Specifically, we…
The time to first crossing for the Poisson counting process with respect to a linear moving barrier with offset is a classic problem, although key results remain scattered across the literature and their equivalence is often unclear. Here…
We investigate the extreme first-passage statistics of $N$ non-interacting random walkers on discrete, hierarchical networks. {By distinguishing between transport limited by escape from localized initial states (injection-limited) and…
For an $n$-element subset $U$ of $\mathbb{Z}^2$, select $x$ from $U$ according to harmonic measure from infinity, remove $x$ from $U$, and start a random walk from $x$. If the walk leaves from $y$ when it first enters $U$, add $y$ to $U$.…
We examine the mean first passage time for a particle driven by highly correlated Gaussian fluctuations to reach one or more predetermined boundaries. We discuss a numerical algorithm to generate power-law correlated fluctuations and apply…
We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions…
We derive an estimate of the rate of formation of dark matter halos per unit volume as a function of the halo mass and redshift of formation. Analytical estimates of the number density of dark matter halos are useful in modeling several…
When a random field $(X_t, \ t\in {\mathbb R}^2)$ is thresholded on a given level $u$, the excursion set is given by its indicator $~1_{[u, \infty)}(X_t)$. The purpose of this work is to study functionals (as established in stochastic…
Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of -4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo…
In the excursion set approach to structure formation initially spherical regions of the linear density field collapse to form haloes of mass $M$ at redshift $z_{\rm id}$ if their linearly extrapolated density contrast, averaged on that…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
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 present a simple and intuitive approximation for solving perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for…
The Schr\"odinger integral-equation approach for calculating the classical first-passage time (C-fpt) probability density is extended to the case of quantum first-passage time (Q-fpt). Using this extension, we have calculated analytically…
I compare the numerical multiplicity function given in Yahagi, Nagashima & Yoshii (2004) with the theoretical multiplicity function obtained by means of the excursion set model and an improved version of the barrier shape obtained in Del…
This research considers Bayesian decision-analytic approaches toward the traversal of an uncertain graph. Namely, a traveler progresses over a graph in which rewards are gained upon a node's first visit and costs are incurred for every edge…
We study the nonlinear evolution of matter overdensities using the spherical collapse model in degenerate higher-order scalar-tensor (DHOST) theories beyond Horndeski, employing the effective field theory (EFT) of dark energy approach. We…
We develop the effective theory of large-scale structure for non-Gaussian initial conditions. The effective stress tensor in the dark matter equations of motion contains new operators, which originate from the squeezed limit of the…
We use a modified version of the Peak Patch excursion set formalism to compute the mass and size distribution of QCD axion miniclusters from a fully non-Gaussian initial density field obtained from numerical simulations of axion string…
This is the first paper of a series of two devoted to develop a practical method to describe the growth history of bound virialized objects in the gravitational instability scenario without resorting to $N$-body simulations. Here we present…