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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…

Probability · Mathematics 2019-05-31 Yu Zhang

We prove non-universality results for first-passage percolation on the configuration model with i.i.d. degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of…

Probability · Mathematics 2015-06-04 Enrico Baroni , Remco van der Hofstad , Julia Komjathy

The Euclidean first-passage percolation (FPP) model of Howard and Newman is a rotationally invariant model of FPP which is built on a graph whose vertices are the points of homogeneous Poisson point process. It was shown that one has…

Probability · Mathematics 2016-11-01 Michael Damron , Xuan Wang

We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean…

Statistical Mechanics · Physics 2023-01-11 Ivan Pompa-Garcia , Rodrigo Castilla , Ralf Metzler , Leonardo Dagdug

The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…

Probability · Mathematics 2023-09-06 Yoann Potiron

For first passage percolation on $\mathbb{Z}^2$ with i.i.d. bounded edge weights, we consider the upper tail large deviation event; i.e., the rare situation where the first passage time between two points at distance $n$, is macroscopically…

Probability · Mathematics 2017-12-05 Riddhipratim Basu , Shirshendu Ganguly , Allan Sly

We investigate the work fluctuations in an overdamped non-equilibrium process that is stopped at a stochastic time. The latter is characterized by a first passage event that marks the completion of the non-equilibrium process. In…

Statistical Mechanics · Physics 2024-03-20 Iago N Mamede , Prashant Singh , Arnab Pal , Carlos E. Fiore , Karel Proesmans

This note proves an upper bound for the fluctuations of a second-class particle in the totally asymmetric simple exclusion process. The proof needs a lower tail estimate for the last-passage growth model associated with the exclusion…

Probability · Mathematics 2007-05-23 Timo Seppalainen

We study a version of first passage percolation on $\mathbb{Z}^d$ where the random passage times on the edges are replaced by contact times represented by random closed sets on $\mathbb{R}$. Similarly to the contact process without…

Probability · Mathematics 2026-02-02 Benedikt Jahnel , Lukas Lüchtrath , Anh Duc Vu

We investigate the statistics of the first-passage time (FPT) to a fractal self-similar boundary of the Koch snowflake. When the starting position is fixed near the absorbing boundary, the FPT distribution exhibits an apparent power-law…

Statistical Mechanics · Physics 2025-07-15 Yilin Ye , Adrien Chaigneau , Denis S. Grebenkov

We consider first passage percolation (FPP) where the vertex weight is given by the exponential of two-dimensional log-correlated Gaussian fields. Our work is motivated by understanding the discrete analog for the random metric associated…

Probability · Mathematics 2017-10-26 Jian Ding , Fuxi Zhang

The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening…

Statistical Mechanics · Physics 2016-09-26 Aljaz Godec , Ralf Metzler

The effect of thermal fluctuations on the temperature dependence of the topological index C1 of the chiral d+id superconducting phase of a two-dimensional single-band model on a triangular lattice is investigated. Thermal fluctuations are…

Superconductivity · Physics 2025-12-10 A. G. Groshev , A. K. Arzhnikov

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 $h_\epsilon$ for…

Probability · Mathematics 2021-03-22 Jian Ding , Ewain Gwynne

In the models of first-passage percolation and directed first-passage percolation on $\mathbb{Z}^d$, we consider a family of i.i.d. random variables indexed by the set of edges of the graph, called passage times. For every vertex $x \in…

Probability · Mathematics 2025-01-31 Antonin Jacquet

We prove results for first-passage percolation on the configuration model with i.i.d. degrees having finite mean, infinite variance and i.i.d. weights with strictly positive support of the form Y=a+X, where a is a positive constant. We…

Probability · Mathematics 2016-09-26 Enrico Baroni , Remco van der Hofstad , Julia Komjathy

Consider first passage percolation on $\mathbb{Z}^d$ with passage times given by i.i.d. random variables with common distribution $F$. Let $t_\pi(u,v)$ be the time from $u$ to $v$ for a path $\pi$ and $t(u,v)$ the minimal time among all…

Probability · Mathematics 2013-12-30 Enrique D. Andjel , Maria Eulalia Vares

We study the diffusion process in the presence of stochastic resetting inside a two-dimensional wedge of top angle $\alpha$, bounded by two infinite absorbing edges. In the absence of resetting, the second moment of the first-passage time…

Statistical Mechanics · Physics 2025-12-01 Fazil Najeeb , Arnab Pal , V. V. Prasad

We study the statistics of first passage times (FPTs) of trajectory observables in both classical and quantum Markov processes. We consider specifically the FPTs of counting observables, that is, the times to reach a certain threshold of a…

Statistical Mechanics · Physics 2024-05-17 George Bakewell-Smith , Federico Girotti , Mădălin Guţă , Juan P. Garrahan

In this paper we consider the first passage percolation with identical and independent exponentially distributions, called the Eden growth model, and we study the upper tail large deviations for the first passage time ${\rm T}$. Our main…

Probability · Mathematics 2020-01-01 Shuta Nakajima