Related papers: Conditional Probabilities in the Excursion Set The…
We discuss an analytic approach for modeling structure formation in sheets, filaments and knots. This is accomplished by combining models of triaxial collapse with the excursion set approach: sheets are defined as objects which have…
In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursion. In this model, the probability of…
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 $U$.…
Any hint of non-gaussianity in the cosmological initial conditions will provide us with a unique window into the physics of early universe. We show that the impact of a small local primordial non-gaussianity (generated on super-horizon…
Usually tunneling is established after imposing some matching conditions on the (time-independent) wave function and its first derivative at the boundaries of a barrier. Here an alternative scheme is proposed to determine tunneling and…
We consider smooth, infinitely divisible random fields $(X(t),t\in M)$, $M\subset {\mathbb{R}}^d$, with regularly varying Levy measure, and are interested in the geometric characteristics of the excursion sets \[A_u=\{t\in M:X(t)>u\}\] over…
The first dark matter halos form by direct collapse from peaks in the matter density field, and evidence from numerical simulations and other analyses suggests that the dense inner regions of these objects largely persist today. These halos…
We present estimates of the nonlinear bias of cosmological halo formation, spanning a wide range in the halo mass from $\sim 10^{5} M_\odot$ to $\sim 10^{12} M_\odot$, based upon both a suite of high-resolution cosmological N-body…
Structures in the Universe are arranged into the cosmic web. Distributions, statistics, and evolutions of the structures can be used as probes for cosmological models. We investigate the number density of voids and dark matter…
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…
Many problems in physics, biology, and economics depend upon the duration of time required for a diffusing particle to cross a boundary. As such, calculations of the distribution of first passage time, and in particular the mean first…
The radial mass distribution of dark matter haloes is investigated within the framework of the spherical infall model. We present a new formulation of spherical collapse including non-radial motions, and compare the analytical profiles with…
We describe and test a new method for creating initial conditions for cosmological N-body dark matter simulations based on second-order Lagrangian perturbation theory (2lpt). The method can be applied to multi-mass particle distributions…
We study a stochastic process $X_t$ related to the Bessel and the Rayleigh processes, with various applications in physics, chemistry, biology, economics, finance and other fields. The stochastic differential equation is $dX_t = (nD/X_t) dt…
In this chapter, we consider the problem of a non-Markovian random walker (displaying memory effects) searching for a target. We review an approach that links the first passage statistics to the properties of trajectories followed by the…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
We use two cosmological simulations of structure formation to study the conditions under which dark matter haloes emerge from the linear density field. Our analysis focuses on matching sites of halo collapse to local density maxima, or…
We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian…
We consider a run-and-tumble particle on a half-line with an absorbing target at the origin. The particle has an internal velocity state that switches between two opposite values at Poisson-distributed times. The position of the particle…
The computation of the probability of the first-passage time through a given threshold of a stochastic process is a classic problem that appears in many branches of physics. When the stochastic dynamics is markovian, the probability admits…