Finitary random interlacements and the Gaboriau–Lyons problem
نویسندگان
چکیده
منابع مشابه
On the Transience of Random Interlacements
Abstract We consider the interlacement Poisson point process on the space of doubly-infinite Zd -valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least one of these trajectories is the graph induced by the random interlacements at level u of Sznitman [9]. We prove that for any u> 0, almost surely, the...
متن کاملOn Pinned Fields, Interlacements, and Random Walk on (z/nz)
We define two families of Poissonian soups of bidirectional trajectories on Z2, which can be seen to adequately describe the local picture of the trace left by a random walk on the two-dimensional torus (Z/NZ)2, started from the uniform distribution, run up to a time of order (N logN)2 and forced to avoid a fixed point. The local limit of the latter was recently established in [6]. Our construc...
متن کاملConnectivity Bounds for the Vacant Set of Random Interlacements
The model of random interlacements on Z, d ≥ 3, was recently introduced in [4]. A non-negative parameter u parametrizes the density of random interlacements on Z. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level u, in the non-percolative regime u > u∗, with u∗ the non-degenerate critical parameter for the percolation of the vaca...
متن کاملRandom Walk on a Discrete Torus and Ran- Dom Interlacements
We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ), d ≥ 3, until uN time steps, u > 0, and the model of random interlacements recently introduced by Sznitman [9]. In particular, we show that for large N , the joint distribution of the local pictures in the neighborhoods of finitely many distant points left by the walk up to t...
متن کاملA lower bound for disconnection by random interlacements
We consider the vacant set of random interlacements on Z, d ≥ 3, in the percolative regime. Motivated by the large deviation principles recently obtained in [13], we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the random interlacements. We derive an asymptotic lower bound, which brings into play tilted interlacements, and relates t...
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: Geometric and Functional Analysis
سال: 2019
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-019-00494-4