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Geometry of the random interlacement

Johan Tykesson (Institutionen för matematiska vetenskaper, matematisk statistik) ; Eviatar Procaccia
Electronic Communications in Probability (1083-589X). Vol. 16 (2011), p. 528-544.
[Artikel, refereegranskad vetenskaplig]

We consider the geometry of random interlacements on the d-dimensional lattice. We use ideas from stochastic dimension theory developed in to prove the following: Given that two vertices x,y belong to the interlacement set, it is possible to find a path between x and y contained in the trace left by at most ⌈d/2⌉ trajectories from the underlying Poisson point process. Moreover, this result is sharp in the sense that there are pairs of points in the interlacement set which cannot be connected by a path using the traces of at most ⌈d/2⌉−1 trajectories.



Denna post skapades 2014-08-12.
CPL Pubid: 201265

 

Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Sannolikhetsteori och statistik

Chalmers infrastruktur