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A wide range of multifield inflationary models generate non-Gaussian initial conditions in which the initial adiabatic fluctuation is of the form (zeta_G + g_{NL} zeta_G^3). We study halo clustering in these models using two different…
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 build a simple analytical model for the bias of dark matter halos that applies to objects defined by an arbitrary density threshold, $200\leq\deltas\leq 1600$, and that provides accurate predictions from low-mass to high-mass halos. We…
We show how correlated steps introduces significant contributions to the modification of the halo mass function in modified gravity models, taking the chameleon models as an example, in the framework of the excursion set approach. This…
Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian)…
We explore the initial conditions for cosmological N-body simulations suitable for calculating the skewness and kurtosis of the density field. In general, the initial conditions based on the perturbation theory (PT) provide incorrect…
This paper studies Gaussian random fields with Mat\'ern covariance functions with smooth parameter $\nu>2$. Two cases of parameter spaces, the Euclidean space and $N$-dimensional sphere, are considered. For such smooth Gaussian fields, we…
We give an analytical form for the weighted correlation function of peaks in a Gaussian random field. In a cosmological context, this approach strictly describes the formation bias and is the main result here. Nevertheless, we show its…
We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean…
The halo occupation distribution (HOD) framework is an empirical method to describe the connection between dark matter halos and galaxies, which is constrained by small scale clustering data. Efficient fitting procedures are required to…
We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that $n_1$, $n_2$, $n_3$, . . . distinct sites are visited at times $t_1$, $t_2$, $t_3$,…
We examine the age-dependence of dark matter halo clustering in an unprecedented accuracy using a set of 7 high-resolution cosmological simulations each with $N=1024^3$ particles. We measure the bias parameters for halos over a large mass…
We establish selection of critical pulled fronts in invasion processes. Our result shows convergence to a pulled front with a logarithmic shift for open sets of steep initial data, including one-sided compactly supported initial conditions.…
We study percolative properties of excursion processes and the discrete Gaussian free field (dGFF) in the planar unit disk. We consider discrete excursion clouds, defined using random walks as a two-dimensional version of random…
In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in…
The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the…
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 derive a Sturm-Liouville system of equations for the exact calculation of the survival probability in first-passage time problems. This system is the one associated with the Wiener-Hopf integral equation obtained from the theory of…
Using the formalism of the spherical infall model the structure of collapsed and virialized dark halos is calculated for a variety of scale-free initial conditions. In spite of the scale-free cosmological nature of the problem, the collapse…
We study the impact of setting initial conditions in numerical simulations using the standard procedure based on the Zel'dovich approximation (ZA). As it is well known from perturbation theory, ZA initial conditions have incorrect second…