发帖
雷达卡
摘要翻译：
当吸收壁以恒定速度$v$运动时，分枝随机游动会随着吸收壁的速度$v$的变化而发生相变。在临界速度$v_c$以下，种群具有非零的生存概率，当种群存活时，其大小呈指数增长。我们研究种群的历史条件是在某个最后时刻有一个幸存者$T$。我们研究了当$T$较大时，$V<V_C$的准平稳状态。为了做到这一点，我们可以构造一个修正的随机过程，它等价于最初的过程，条件是在最后时刻有一个幸存者$T$。然后我们用这个结构证明了当$v\到v_c$时，准平稳区域的性质是普遍的。我们还精确地解决了该问题的一个简单版本，即指数模型，对该模型的准平稳区的研究可以归结为对单个一维映射的分析。
---
英文标题：
《Quasi-stationary regime of a branching random walk in presence of an
absorbing wall》
---
作者：
Damien Simon and Bernard Derrida
---
最新提交年份：
2008
---
分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
一级分类：Quantitative Biology 数量生物学
二级分类：Populations and Evolution 种群与进化
分类描述：Population dynamics, spatio-temporal and epidemiological models, dynamic speciation, co-evolution, biodiversity, foodwebs, aging; molecular evolution and phylogeny; directed evolution; origin of life
种群动力学；时空和流行病学模型；动态物种形成；协同进化；生物多样性；食物网；老龄化；分子进化和系统发育；定向进化；生命起源
--
---
英文摘要：
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival probability and when the population survives its size grows exponentially. We investigate the histories of the population conditioned on having a single survivor at some final time $T$. We study the quasi-stationary regime for $v<v_c$ when $T$ is large. To do so, one can construct a modified stochastic process which is equivalent to the original process conditioned on having a single survivor at final time $T$. We then use this construction to show that the properties of the quasi-stationary regime are universal when $v\to v_c$. We also solve exactly a simple version of the problem, the exponential model, for which the study of the quasi-stationary regime can be reduced to the analysis of a single one-dimensional map.
---
PDF链接：
https://arxiv.org/pdf/710.3689
京公网安备 11010802022788号
