Large deviations for intersection local times in critical dimension

Castell, Fabienne

Ann. Probab., Tome 38 (2010) no. 1, p. 927-953 / Harvested from Project Euclid

Résumé

Let (X_t, t≥0) be a continuous time simple random walk on ℤ^d (d≥3), and let l_T(x) be the time spent by (X_t, t≥0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I_T=∑_x∈ℤ^dl_T(x)^q in the critical case q=d/(d−2). When q is integer, we obtain similar results for the intersection local times of q independent simple random walks.

Publié le : 2010-03-15
Classification: Large deviations, intersection local times, 60F10, 60J15, 60J55

@article{1268143536,
     author = {Castell, Fabienne},
     title = {Large deviations for intersection local times in critical dimension},
     journal = {Ann. Probab.},
     volume = {38},
     number = {1},
     year = {2010},
     pages = { 927-953},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1268143536}
}

Castell, Fabienne. Large deviations for intersection local times in critical dimension. Ann. Probab., Tome 38 (2010) no. 1, pp.  927-953. http://gdmltest.u-ga.fr/item/1268143536/