Related papers: Lower bounds on non-random fluctuations in planar …
Extra-galactic sources of photons have been used to constrain space-time quantum fluctuations in the Universe. In these proposals, the fundamental "fuzziness" of distance caused by space-time quantum fluctuations has been directly…
We study the first passage times of discrete-time branching random walks in ${\mathbb R}^d$ where $d\geq 1$. Here, the genealogy of the particles follows a supercritical Galton-Watson process. We provide asymptotics of the first passage…
In this paper, we study some properties of optimal paths in the first passage percolation on $\Z^d$ and show the followings: (1) the number of optimal paths has an exponential growth if the distribution has an atom; (2) the means of…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to a point. We also…
We prove fluctuation bounds for the particle current in totally asymmetric zero range processes in one dimension with nondecreasing, concave jump rates whose slope decays exponentially. Fluctuations in the characteristic directions have…
First passage time plays a fundamental role in dynamical characterization of stochastic processes. Crucially, our current understanding on the problem is almost entirely relies on the theoretical formulations, which assume the processes…
We consider the first passage percolation model on the square lattice with an edge weight distribution F. In this paper, we consider the number of optimal paths for two points separated by a long distance. We show that there is a phase…
We consider first-passage percolation with positive, stationary-ergodic weights on the square lattice $\mathbb{Z}^d$. Let $T(x)$ be the first-passage time from the origin to a point $x$ in $\mathbb{Z}^d$. The convergence of the scaled…
First passage percolation on $\mathbb{Z}^2$ is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage…
We study the rate of convergence in the Shape Theorem of first-passage percolation, obtaining the precise asymptotic rate of decay for the probability of linear order deviations under a moment condition. Our results are stated for a given…
We establish asymptotic diffusion limits of the non-classical transport equation derived in [E. W. Larsen, A generalized Boltzmann equation for non-classical particle transport, Joint international topical meeting on mathematics &…
Let $d\in\mathbb N$, $\alpha\in\mathbb R$, and let $f :\mathbb R^d\setminus \{0\} \rightarrow (0,\infty)$ be locally Lipschitz and positively homogeneous of degree $\alpha$ (e.g. $f$ could be the $\alpha$th power of a norm on $\mathbb…
By optimal fluctuation method, we study short-time distribution $P(\mathcal{A}=A)$ of the functionals, $\mathcal{A}=\int_{0}^{t_f} x^n(t) dt$, along constrained trajectories of random acceleration process for a given time duration $t_f$,…
We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically…
We derive an approximate but fully explicit formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape in a general elongated domain in the plane. Our approximation combines conformal mapping, boundary…
A class of algorithms in discrete space and continuous time for Brownian first passage time estimation is considered. A simple algorithm is derived that yields exact mean first passage times (MFPT) for linear potentials in one dimension,…
We relate discrepancy theory with the classic scheduling problems of minimizing max flow time and total flow time on unrelated machines. Specifically, we give a general reduction that allows us to transfer discrepancy bounds in the prefix…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
The first passage time (FPT) problem is studied for superstatistical models assuming that the mesoscopic system dynamics is described by a Fokker-Planck equation. We show that all moments of the random intensive parameter associated to the…