In high dimensions two independent simple random walks have only a finite number of intersections. I describe the main result obtained in a joint paper with Xia Chen in which we determine the exact upper tail behaviour of the intersection local time.
@article{ACIRM_2010__2_1_27_0,
author = {Peter M\"orters},
title = {Upper tail asymptotics for the intersection local times of random walks in high dimensions},
journal = {Actes des rencontres du CIRM},
publisher = {CIRM},
volume = {2},
number = {1},
year = {2010},
pages = {27-29},
doi = {10.5802/acirm.20},
language = {en},
url = {acirm.centre-mersenne.org/item/ACIRM_2010__2_1_27_0/}
}
Mörters, Peter. Upper tail asymptotics for the intersection local times of random walks in high dimensions. Actes des rencontres du CIRM, Tome 2 (2010) no. 1, pp. 27-29. doi : 10.5802/acirm.20. https://acirm.centre-mersenne.org/item/ACIRM_2010__2_1_27_0/
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