Related papers: The Excursion set approach: Stratonovich approxima…
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…
We present measurements of the number density of voids in the dark matter distribution from a series of N-body simulations of a \Lambda CDM cosmology. We define voids as spherical regions of \rho_v = 0.2\rho_m around density minima in order…
We combine the physics of the ellipsoidal collapse model with the excursion set theory to study the shapes of dark matter halos. In particular, we develop an analytic approximation to the nonlinear evolution that is more accurate than the…
Researching elliptic analogues for equalities and formulas is a new trend in enumerative combinatorics which has followed the previous trend of studying $q$-analogues. Recently Schlosser proposed a lattice path model in the square lattice…
We obtain approximations for the CDM particle trajectories starting from Lagrangian Perturbation Theory. These estimates for the CDM trajectories result in approximations for the density in real and redshift space, as well as for the…
Evolution of genus density is calculated from Gaussian initial conditions using Zel'dovich approximation. A new approach is introduced which formulates the desired quantity in a rotationally invariant manner. It is shown that normalized…
We consider conservative cross-diffusion systems for two species where individual motion rates depend linearly on the local density of the other species. We develop duality estimates and obtain stability and approximation results. We first…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from…
The formation of cosmological large-scale structure is usually described in terms of the evolution of density fluctuations and their statistical measures, such as the power spectrum and correlation function. However, these statistics…
We develop an excursion theory for Brownian motion indexed by the Brownian tree, which in many respects is analogous to the classical It\^o theory for linear Brownian motion. Each excursion is associated with a connected component of the…
The large-scale structure is a major source of cosmological information. However, next-generation photometric galaxy surveys will only provide a distorted view of cosmic structures due to large redshift uncertainties. To address the need…
We analyze the properties of searches devoted to finding planetary transits by observing simple stellar systems, such as globular clusters, open clusters, and the Galactic bulge. We develop the analytic tools necessary to predict the number…
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 revisit an old minor topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and…
Matter evolved under influence of gravity from minuscule density fluctuations. Non-perturbative structure formed hierarchically over all scales, and developed non-Gaussian features in the Universe, known as the Cosmic Web. To fully…
Context: Analyzing the large-scale structure (LSS) with galaxy surveys demands accurate structure formation models. Such models should ideally be fast and have a clear theoretical framework to rapidly scan a variety of cosmological…
Constrained realisations of Gaussian random fields are used in cosmology to design special initial conditions for numerical simulations. We review this approach and its application to density peaks providing several worked-out examples. We…
One of the main unsolved problems of cosmology is how to maximize the extraction of information from nonlinear data. If the data are nonlinear the usual approach is to employ a sequence of statistics (N-point statistics, counting statistics…
The problem of how to estimate diffusion on a graph effectively is of importance both theoretically and practically. In this paper, we make use of two widely studied indices, geodesic distance and mean first-passage time ($MFPT$) for random…