Related papers: Fluctuations of Transverse Increments in Two-dimen…
We consider the bilocal conductivity tensor, the two-probe conductance and its fluctuations for a disordered phase-coherent two-dimensional system of non-interacting electrons in the presence of a magnetic field, including correctly the…
We study a natural growth process with competition, which was recently introduced to analyze MDLA, a challenging model for the growth of an aggregate by diffusing particles. The growth process consists of two first-passage percolation…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
We consider the multi-time correlation and covariance structure of a random surface growth with a wall introduced in arXiv:0904.2607. It is shown that the correlation functions associated with the model along space-like paths have…
The approach the first-passage time (FPT) of a random process to a certain level is applied to the description of radiation-enhanced diffusion. This is an integral approach to describing the problem of radiation-enhanced diffusion, which…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by infinite peaks on a coherently constructed potential energy landscape. It is then important to ask what such…
We study analytically the correlations between the positions of tagged particles in the random average process, an interacting particle system in one dimension. We show that in the steady state the mean squared auto-fluctuation of a tracer…
For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For…
First-passage percolation is the study of the metric space $(\mathbb{Z}^d,T)$, where $T$ is a random metric defined as the weighted graph metric using random edge-weights $(t_e)_{e\in \mathcal{E}^d}$ assigned to the nearest-neighbor edges…
Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two…
We consider the first passage percolation model in Z2 with a distribution F for 0 < F (0) < pc. In this paper, we solve the height problem.
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…
We introduce and study derivatives in first-passage percolation with edge weights given by i.i.d. random variables supported on ${a,b}$. We show that the variance of the passage time can be expressed in terms of these derivatives. We…
We develop a method based on martingales to study first-passage problems of time-additive observables exiting an interval of finite width in a Markov process. In the limit that the interval width is large, we derive generic expressions for…
The Inverse First Passage time problem seeks to determine the boundary corresponding to a given stochastic process and a fixed first passage time distribution. Here, we determine the numerical solution of this problem in the case of a two…
The $n$-dimensional binary hypercube is the graph whose vertices are the binary $n$-tuples $\{0, 1\}^n$ and where two vertices are connected by an edge if they differ at exactly one coordinate. We prove that if the edges are assigned…
Liouville first passage percolation (LFPP) with parameter $\xi > 0$ is the family of random distance functions (metrics) $(D_h^{\epsilon})_{\epsilon > 0}$ on $\mathbb{C}$ obtained heuristically by integrating $e^{\xi h}$ along paths, where…
We study diffusion with a bias towards a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the…
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…