Related papers: Excursion Set Theory for generic moving barriers a…
We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in…
First-passage time problems are ubiquitous across many fields of study including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage time…
We consider a general class of maps of the interval having Lyapunov subexponential instability $|\delta x_{t}|\sim|\delta x_{0}|\exp[\Lambda_{t}(x_{0})\zeta(t)]$, where $\zeta(t)$ grows sublinearly as $t\rightarrow\infty$. We outline here a…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
In this paper we extend results of L.A. Shepp by finding explicit formulas for the first passage probability $F_{a,b}(T\, |\, x)={\rm Pr}(S(t)<a+bt \text{ for all } t\in[0,T]\,\, | \,\,S(0)=x)$, for all $T>0$, where $S(t)$ is a Gaussian…
We investigate the impact of early-time initial conditions on nonlinear structure formation and evolution within the framework of the semi-analytical Excursion Set Theory (EST). Our analysis reveals that adding a Gaussian bump to the…
First-passage times provide invaluable insight into fundamental properties of stochastic processes. Yet, various forms of gating mask first-passage times and differentiate them from actual detection times. For instance, imperfect conditions…
The gravitational collapse of collisionless matter leads to shell-crossing singularities that challenge the applicability of standard perturbation theory. Here, we present the first fully perturbative approach in three dimensions by using…
We develop a practical framework for distinguishing diffusive stochastic processes from deterministic signals using only a single discrete time series. Our approach is based on classical excursion and crossing theorems for continuous…
The cosmological mass function problem is analyzed in full detail in the case of 1D gravity, with analytical, semi-analytical and numerical techniques. The extended Press & Schechter theory is improved by detailing the relation between…
We calculate the mean shape of transition paths and first-passage paths based on the one-dimensional Fokker-Planck equation in an arbitrary free energy landscape including a general inhomogeneous diffusivity profile. The transition path…
We investigate the dependence of the mass function of dark-matter haloes on their environment within the cosmic web of large-scale structure. A dependence of the halo mass function on large-scale mean density is a standard element of…
We present an analytical model for the non-spherical collapse of overdense regions out of a Gaussian random field of initial cosmological perturbations. The collapsing region is treated as an ellipsoid of constant density, acted upon by the…
We investigate cosmic structure formation in the framework of a path-integral formulation of an $N$-particle ensemble in phase space, dubbed Resummed Kinetic Field Theory (RKFT), up to one-loop perturbative order. In particular, we compute…
We discuss a new algorithm to generate multi-scale initial conditions with multiple levels of refinements for cosmological "zoom-in" simulations. The method uses an adaptive convolution of Gaussian white noise with a real space transfer…
Many natural systems exhibit dynamics characterized by alternating phases or recurring sets of states. Describing the fluctuations of such systems over stochastic trajectories is necessary across diverse fields, from biological motors to…
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…
Computing collision-free trajectories is of prime importance for safe navigation. We present an approach for computing the collision probability under Gaussian distributed motion and sensing uncertainty with the robot and static obstacle…
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…
We study structure formation in the presence of primordial non-Gaussianity of the local type with parameters f_NL and g_NL. We show that the distribution of dark-matter halos is naturally described by a multivariate bias scheme where the…