اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Brownian Net with Killing
131
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 Poisson intensity measure to the continuum counterparts.
قيم البحث
اقرأ أيضاً
The Brownian map is a fundamental object in mathematics, in some sense a 2-dimensional analogue of Brownian motion. Here we briefly explain this object and a bit of its history.
We derive the explicit form of the martingale representation for square-integrable processes that are martingales with respect to the natural filtration of the super-Brownian motion. This is done by using a weak extension of the Dupire derivative for functionals of superprocesses.
We consider the Brownian interlacements model in Euclidean space, introduced by A.S. Sznitman in cite{sznitman2013scaling}. We give estimates for the asymptotics of the visibility in the vacant set. We also consider visibility inside the vacant set o
f the Brownian excursion process in the unit disc and show that it undergoes a phase transition regarding visibility to infinity as in cite{benjamini2009visibility}. Additionally, we determine the critical value and that there is no visibility to infinity at the critical intensity.
We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of $-sqrt{2}$. Kesten (1978) showed that almost surely this process eventually d
ies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time $t$. These bounds improve upon results of Kesten (1978), and partially confirm nonrigorous predictions of Derrida and Simon (2007).
We consider critical branching Brownian motion with absorption, in which there is initially a single particle at $x > 0$, particles move according to independent one-dimensional Brownian motions with the critical drift of $-sqrt{2}$, and particles ar
e absorbed when they reach zero. Here we obtain asymptotic results concerning the behavior of the process before the extinction time, as the position $x$ of the initial particle tends to infinity. We estimate the number of particles in the system at a given time and the position of the right-most particle. We also obtain asymptotic results for the configuration of particles at a typical time.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
