Replica overlap and covering time for the Wiener sausages among Poissonian obstacles
نویسندگان
چکیده
منابع مشابه
Replica overlap and covering time for the Wiener sausages among Poissonian obstacles
We study two objects concerning the Wiener sausage among Poissonian obstacles. The first is the asymptotics for the replica overlap, which is the intersection of two independent Wiener sausages. We show that it is asymptotically equal to their union. This result confirms that the localizing effect of the media is so strong as to completely determine the motional range of particles. The second i...
متن کاملAsymptotics for the Wiener sausage among Poissonian obstacles
We consider the Wiener sausage among Poissonian obstacles. The obstacle is called hard if Brownian motion entering the obstacle is immediately killed, and is called soft if it is killed at certain rate. It is known that Brownian motion conditioned to survive among obstacles is confined in a ball near its starting point. We show the weak law of large numbers, large deviation principle in special...
متن کاملOn the Boolean model of Wiener sausages
The Boolean model of Wiener sausages is a random closed set that can be thought of as a random collection of parallel neighborhoods of independent Wiener paths in space. It describes e.g. the target detection area of a network of sensors moving according to the Brownian dynamics whose initial locations are chosen in the medium at random. In the paper, the capacity functional of this Boolean mod...
متن کاملBranching Brownian Motion with “mild” Poissonian Obstacles
We study a spatial branching model, where the underlying motion is Brownian motion and the branching is affected by a random collection of reproduction blocking sets called mild obstacles. We show that the quenched local growth rate is given by the branching rate in the ‘free’ region . When the underlying motion is an arbitrary diffusion process, we obtain a dichotomy for the local growth that ...
متن کاملStrong approximations of three-dimensional Wiener sausages
In this paper we prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall [10]’s fine L-norm estimates betwee...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 2008
ISSN: 2156-2261
DOI: 10.1215/kjm/1250271422