Baire Categorical Aspects of First Passage Percolation
Megjelenés dátuma: 2017
Kulcsszó: mathemathics
Matematikus TDK
TDK dolgozat
Matematikus TDK
TDK dolgozat
Absztrakt:
In the previous decades, the theory of first passage percolation became a
highly important area of probability theory. In this work, we will observe what can be
said about the corresponding structure if we forget about the probability measure defined
on the product space of edges and simply consider topology in the terms of residuality.
We focus on interesting questions arising in the probabilistic setup that make sense in
this setting, too. We will see that certain classical almost sure events, as the existence of
geodesics have residual counterparts, while the notion of the limit shape or time constants
gets as chaotic as possible.