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abstract:
The model of Brownian motion in Poissonian potential
describes a typical trajectory of a Brownian particle
surviving from being attracted by the obstacles randomly
located in the space (think about the stars in the universe).
In the existing literature, the random
potential is defined as the convolution between a Poissonian field and
a bounded and locally supported function.
According to the Newton's law of universal attraction and some
other related laws in physics, the most natural way of constructing
the random potential is to define it as the Riesz potential of
the Poissonian field. On the other hand, the Riesz potential of
the Poissonian field blows up.
In this talk, this problem will be fixed by the way of renormalization.
In addition, some asymptotic patterns of our models will be established
and more problems will be asked. Part of the talk is based on some
collaborative works with Kulic and Rosen. |
