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We consider the problem of stochastic flow of multiple particles traveling on a closed loop, with a constraint that particles move without passing. We use a Markov chain description that reduces the problem to a generalized random walk on a…
We extend the matter bounce scenario to a more general theory in which the background dynamics and cosmological perturbations are generated by a $k$-essence scalar field with an arbitrary sound speed. When the sound speed is small, the…
In studies of the environmental dependence of structure formation, the large scale environment is often thought of as providing an effective background cosmology: e.g. the formation of structure in voids is expected to be just like that in…
We investigate the trajectory-level dynamics of a double quantum dot system using the newly developed formalism of stochastic excursions. This approach extends full counting statistics by enabling a filtering of complex trajectories into…
In the context of the random first order transition theory we use an extended mode coupling theory of the glass transition that includes activated events to account for spatiotemporal structures in aging and rejuvenating glasses. We…
In this article, we show that a stochastic form of scale-dependent halo bias arises in multi-source inflationary models, where multiple fields determine the initial curvature perturbation. We derive this effect for general non-Gaussian…
We present an analytic model for the splashback mass function of dark matter halos, which is parameterized by a single coefficient and constructed in the framework of the generalized excursion set theory and the self-similar spherical…
We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for…
Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past. In this paper, we introduce a new class of problems: transport in Hamiltonian systems with slowly changing phase space structure that are…
We construct a continuous-time non-commutative random walk on $U(\mathfrak{gl}_N)$ with dilation maps $U(\mathfrak{gl}_N)\rightarrow L^2(U(N))^{\otimes\infty}$. This is an analog of a continuous-time non-commutative random walk on the group…
We explore first-passage phenomenology for biased active processes with a renewal-type structure, focusing in particular on paradigmatic run-and-tumble models in both discrete and continuous state spaces. In general, we show there is no…
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 present a pedagogical review of the halo model, a flexible framework that can describe the distribution of matter and its tracers on non-linear scales for both conventional and exotic cosmological models. We start with the premise that…
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…
We develop an asymptotic approximation and bounds for the traveling salesman problem with time slots, i.e. when the time windows of points to visit are a partition of a given time horizon. Although this problem is relevant in several…
We study exit times from time-dependent domains under joint perturbations of the trajectory and the domain. Representing a moving domain by a continuous barrier $\Phi$ on space-time, we reduce the exit problem to a one-dimensional…
In this work we consider a stochastic movement process with random resets to the origin followed by a random residence time there before the walker restarts its motion. First, we study the transport properties of the walker, we derive an…
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 present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…