The Brownian Net with Killing
The Brownian Net with Killing
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带有杀戮的布朗网
DOI：
10.1016/j.spa.2014.09.018
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
E. Schertzer
中科院分区：
文献类型：
--
作者：
C. Newman;Krishnamurthi Ravishankar;E. Schertzer
出于其相关性的研究扰动的一维选民模型，包括随机Potts模型在低温下，我们考虑扩散重新缩放合并随机游动分支和杀戮。我们的主要结果是收敛到一个新的连续过程，其中的随机时空路径的Sun-SwartBrownian网终止于泊松云的杀戮点。我们还证明了存在一个渗滤过渡的杀伤率的变化。收敛的关键问题是离散模型的杀伤点和它们的强度测量与连续对应物的关系：这些收敛问题使得布朗网比布朗网更难添加杀伤。
Motivated by its relevance for the study of perturbations of one-dimensional voter models, including stochastic Potts models at low temperature, we consider diffusively rescaled coalescing random walks with branching and killing. Our main result is convergence to a new continuum process, in which the random space–time paths of the Sun–Swart Brownian net are terminated at a Poisson cloud of killing points. We also prove existence of a percolation transition as the killing rate varies. Key issues for convergence are the relations of the discrete model killing points and their intensity measure to the continuum counterparts: these convergence issues make the addition of killing considerably more difficult for the Brownian net than for the Brownian web.