Open Access
September 2009 Upper bound on the disconnection time of discrete cylinders and random interlacements
Alain-Sol Sznitman
Ann. Probab. 37(5): 1715-1746 (September 2009). DOI: 10.1214/09-AOP450


We study the asymptotic behavior for large N of the disconnection time TN of a simple random walk on the discrete cylinder (ℤ/Nℤ)d×ℤ, when d≥2. We explore its connection with the model of random interlacements on ℤd+1 recently introduced in [Ann. Math., in press], and specifically with the percolative properties of the vacant set left by random interlacements. As an application we show that in the large N limit the tail of TN/N2d is dominated by the tail of the first time when the supremum over the space variable of the Brownian local times reaches a certain critical value. As a by-product, we prove the tightness of the laws of TN/N2d, when d≥2.


Download Citation

Alain-Sol Sznitman. "Upper bound on the disconnection time of discrete cylinders and random interlacements." Ann. Probab. 37 (5) 1715 - 1746, September 2009.


Published: September 2009
First available in Project Euclid: 21 September 2009

zbMATH: 1179.60025
MathSciNet: MR2561432
Digital Object Identifier: 10.1214/09-AOP450

Primary: 60G50 , 60K35 , 82C41

Keywords: disconnection , discrete cylinders , Random interlacements , Random walks

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5 • September 2009
Back to Top