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Related papers: The Frog Model on $\mathbb{Z}$ with Discrete Weibu…

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We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…

Probability · Mathematics 2010-11-09 Herve Guiol , Fabio P. Machado , Rinaldo B. Schinazi

We provide an asymptotic analysis of a nonlinear integro-differential equation describing the evolutionary dynamics of a population which reproduces sexually and which is subject to selection and competition. The sexual reproduction is…

Analysis of PDEs · Mathematics 2023-09-19 J Guerand , M Hillairet , S Mirrahimi

One-dimensional disordered systems with a random potential of a small amplitude and short-range correlations are considered near the initial band edge. The evolution equation is obtained for the mutual ditribution P(\rho,\psi) of the…

Disordered Systems and Neural Networks · Physics 2023-10-24 I. M. Suslov

We study the frog model on $\mathbb{Z}^d$ with drift in dimension $d \geq 2$ and establish the existence of transient and recurrent regimes depending on the transition probabilities. We focus on a model in which the particles perform…

Probability · Mathematics 2021-04-27 Christian Döbler , Nina Gantert , Thomas Höfelsauer , Serguei Popov , Felizitas Weidner

We study the the survival probability P(t) upto time t, of a test particle moving in a fluctuating external field. The particle moves according to some prescribed deterministic or stochastic rules and survives as long as the external field…

Statistical Mechanics · Physics 2009-10-30 Satya N. Majumdar , Stephen J. Cornell

We consider the continuous-time frog model on $\mathbb{Z}$. At time $t = 0$, there are $\eta (x)$ particles at $x\in \mathbb{Z}$, each of which is represented by a random variable. In particular, $(\eta(x))_{x \in \mathbb{Z} }$ is a…

Probability · Mathematics 2023-09-28 Viktor Bezborodov , Luca Di Persio , Peter Kuchling

We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on $\mathbb{Z}^d$ according to a contact process with parameter $\lambda>0$. With probability $p \in [0,1]$ an offspring is fertile…

Probability · Mathematics 2025-11-18 Sonia Velasco

We consider a random walk with death in $[-N,N]$ moving in a time dependent environment. The environment is a system of particles which describes a current flux from $N$ to $-N$. Its evolution is influenced by the presence of the random…

Probability · Mathematics 2015-07-29 Anna De Masi , Errico Presutti , Dimitrios Tsagkarogiannis , Maria Eulalia Vares

The reproduction speed of a continuous-time branching random walk is proportional to a positive parameter $\lambda$. There is a threshold for $\lambda$, which is called $\lambda_w$, that separates almost sure global extinction from global…

Probability · Mathematics 2017-04-28 Daniela Bertacchi , Cristian F. Coletti , Fabio Zucca

The frog model is a system of interacting random walks. Initially, there is one particle at each vertex of a connected graph $\mathcal{G}$. All particles are inactive at time zero, except for the one which is placed at the root of…

Probability · Mathematics 2022-10-12 Gustavo O. de Carvalho , Fábio P. Machado

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing…

Populations and Evolution · Quantitative Biology 2015-06-05 Samir Suweis , Andrea Rinaldo , Amos Maritan

In this paper, we investigate accelerated life testing (ALT) models based on the Weibull distribution with stress-dependent shape and scale parameters. Temperature and voltage are treated as stress variables influencing the lifetime…

Methodology · Statistics 2026-01-13 Rahul Konar , Ramnivas Jat , Neeraj Joshi , Raghu Nandan Sengupta

The occupation time of an age-dependent branching particle system in $\Rd$ is considered, where the initial population is a Poisson random field and the particles are subject to symmetric $\alpha$-stable migration, critical binary branching…

Probability · Mathematics 2009-03-12 José Alfredo López-Mimbela , Antonio Murillo Salas

We study an interacting random walk system on Z where at time 0 there is an active particle at 0 and one inactive particle on each site $n \ge 1$. Particles become active when hit by another active particle. Once activated, the particle…

Probability · Mathematics 2012-12-20 Daniela Bertacchi , Fabio Prates Machado , Fabio Zucca

This article is aimed at the investigation of some properties of the Weibull cumulative exposure model on multiple-step step-stress accelerated life test data. Although the model includes a probabilistic idea of Miner's rule in order to…

Statistics Theory · Mathematics 2012-10-23 Yoshio Komori

The analysis of progressively censored data has received considerable attention in the last few years. In this paper we consider the joint progressive censoring scheme for two populations. It is assumed that the lifetime distribution of the…

Methodology · Statistics 2017-06-26 Shuvashree Mondal , Debasis Kundu

We consider the extreme eigenvalues of the sample covariance matrix $Q=YY^*$ under the generalized elliptical model that $Y=\Sigma^{1/2}XD.$ Here $\Sigma$ is a bounded $p \times p$ positive definite deterministic matrix representing the…

Methodology · Statistics 2023-04-20 Xiucai Ding , Jiahui Xie , Long Yu , Wang Zhou

We introduce a parameter $p$, called partial survival, in the persistence of stochastic processes and show that for smooth processes the persistence exponent $\theta(p)$ changes continuously with $p$, $\theta(0)$ being the usual persistence…

Statistical Mechanics · Physics 2009-10-31 Satya N. Majumdar , Alan J. Bray

The use of flat or weakly informative priors is popular due to the objective a priori belief in the absence of strong prior information. In the case of the Weibull model the improper uniform, equal parameter gamma and joint Jeffrey's priors…

Methodology · Statistics 2020-02-18 Janet van Niekerk , Haakon Bakka , Haavard Rue

In this paper, we consider a free boundary multi-layer tumor model that incorporates a $T-$periodic provision of external nutrients $\Phi(t)$. The simplified model contains three parameters: the mean of periodic external nutrients…

Analysis of PDEs · Mathematics 2025-08-28 Wenhua He , Mingxin Wang , Ruixiang Xing