Related papers: Fluctuations of Transverse Increments in Two-dimen…
We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of…
We consider a Markovian growth process on a partially ordered set $\Lambda$, equivalent to last passage percolation (LPP) with independent (not necessarily identical) exponentially distributed weights on the elements of $\Lambda$. Such a…
In this paper, we study random walks on a small-world scale-free network, also called as pseudofractal scale-free web (PSFW), and analyze the volatilities of first passage time (FPT) and first return time (FRT) by using the variance and the…
We determine the asymptotic speed of the first-passage percolation process on some ladder-like graphs (or width-2 stretches) when the times associated with different edges are independent and exponentially distributed but not necessarily…
In a recent breakthrough work, Chatterjee [Ann. of Math. (2) 177 (2013) 663-697] proved a long standing conjecture that relates the transversal exponent $\xi$ and the fluctuation exponent $\chi$ in first-passage percolation on…
In 1999, Zhang proved that, for first passage percolation on the square lattice $\mathbb{Z}^2$ with i.i.d. non-negative edge weights, if the probability that the passage time distribution of an edge $P(t_e = 0) =1/2 $, the critical value…
Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…
Liouville first passage percolation (LFPP) with parameter $\xi > 0$ is the family of random distance functions $\{D_h^\epsilon\}_{\epsilon >0}$ on the plane obtained by integrating $e^{\xi h_\epsilon}$ along paths, where…
The scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice in the critical region are investigated. We study numerically two scaling functions:…
Last passage percolation (LPP) in an $n\times n$ lower triangular domain has nice connections with various generalizations of Schur measures. LPP along an anti-diagonal, from $(1,n)$ to $(n,1)$, gives a distribution of a highest column of a…
We consider a last-passage directed percolation model in $Z_+^2$, with i.i.d. weights whose common distribution has a finite $(2+p)$th moment. We study the fluctuations of the passage time from the origin to the point $\big(n,n^{\lfloor a…
In this paper we study first-passge percolation models on Delaunay triangulations. We show a sufficient condition to ensure that the asymptotic value of the rescaled first-passage time, called the time constant, is strictly positive and…
We consider a one-dimensional fluctuating interfacial profile governed by the Edwards-Wilkinson or the stochastic Mullins-Herring equation for periodic, standard Dirichlet and Dirichlet no-flux boundary conditions. The minimum action path…
In this paper we consider first passage percolation on the square lattice \(\mathbb{Z}^d\) with passage times that are independent and have bounded \(p^{th}\) moment for some \(p > 6(1+d),\) but not necessarily identically distributed. For…
Consider the indicator function $f$ of a two-dimensional percolation crossing event. In this paper, the Fourier transform of $f$ is studied and sharp bounds are obtained for its lower tail in several situations. Various applications of…
Height fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently there has been spectacular progress in the studies of this quantity for the…
A simple lemma bounds $\mathrm{s.d.}(T)/\mathbb{E} T$ for hitting times $T$ in Markov chains with a certain strong monotonicity property. We show how this lemma may be applied to several increasing set-valued processes. Our main result…
We consider the following oriented percolation model of $\mathbb {N} \times \mathbb{Z}^d$: we equip $\mathbb {N}\times \mathbb{Z}^d$ with the edge set $\{[(n,x),(n+1,y)] | n\in \mathbb {N}, x,y\in \mathbb{Z}^d\}$, and we say that each edge…
We demonstrate that the first arrival time in dispersive processes in self-affine fractures are governed by the same length scale characterizing the fractures as that which controls their permeability. In one-dimensional channel flow this…
We investigate two coupled properties of Levy stable random motions: The first passage times (FPTs) and the first passage leapovers (FPLs). While, in general, the FPT problem has been studied quite extensively, the FPL problem has hardly…