Related papers: Conditional Probabilities in the Excursion Set The…
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…
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…
Collision prediction in a dynamic and unknown environment relies on knowledge of how the environment is changing. Many collision prediction methods rely on deterministic knowledge of how obstacles are moving in the environment. However,…
The Hubble tension may introduce a new course of action to revise the standard $\Lambda$CDM model to unravel dark energy and dark matter physics. The Hubble parameter can be reconstructed by late-time observations of the background…
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 motion of a lazy Pearson walker is studied with different probability ($p$) of jump in two and three dimensions. The probability of exit ($P_e$) from a zone of radius $r_e$, is studied as a function of $r_e$ with different values of…
The clustering of dark matter halos depends not only on their mass, the so-called primary bias, but also on their internal properties, the so-called secondary bias. While the former effect is well-understood within the Press-Schechter (PS)…
We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity. In this study we focus on understanding the matter clustering at several redshifts. The primordial non-Gaussianity is modeled as…
In the standard picture of cosmology, the galaxies reside in dark matter (DM) halos. DM halos are distributed in the cosmic web in different environments. The luminosity of the galaxies in different environments can be used as a probe to…
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 solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…
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…
Let $X = \{X(t): t\in T \}$ be a non-centered, unit-variance, smooth Gaussian random field indexed on some parameter space $T$, and let $A_u(X,T) = \{t\in T: X(t)\geq u\}$ be the excursion set of $X$ exceeding level $u$. Under certain…
We develop a novel approach in exploring the joint dependence of halo bias on multiple halo properties using Gaussian process regression. Using a $\Lambda$CDM $N$-body simulation, we carry out a comprehensive study of the joint bias…
We study the scale-dependence of halo bias in generic (non-local) primordial non-Gaussian (PNG) initial conditions of the type motivated by inflation, parametrized by an arbitrary quadratic kernel. We first show how to generate non-local…
Nonspherical collapse is modelled, under the Zeldovich approximation, by six-dimensional random walks of the initial deformation tensor field. The collapse boundary adopted here is a slightly-modified version of that proposed by Chiueh and…
Motivated by the dynamics of resonant neurons we consider a differentiable, non-Markovian random process $x(t)$ and particularly the time after which it will reach a certain level $x_b$. The probability density of this first passage time is…
An interesting statistical problem is to find regions where some studied process exceeds a certain level. Estimating such regions so that the probability for exceeding the level in the entire set is equal to some predefined value is a…
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…
Continued great efforts have been dedicated towards high-quality trajectory generation based on optimization methods, however, most of them do not suitably and effectively consider the situation with moving obstacles; and more particularly,…