Heat kernel for random walk trace on ℤ3 and ℤ4
Shiraishi, Daisuke
Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, p. 1001-1024 / Harvested from Project Euclid
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We study the simple random walk X on the range of simple random walk on ℤ3 and ℤ4. In dimension four, we establish quenched bounds for the heat kernel of X and max0≤k≤n|Xk| which require extra logarithmic correction terms to the higher-dimensional case. In dimension three, we demonstrate anomalous behavior of X at the quenched level. In order to establish these estimates, we obtain several asymptotic estimates for cut times of simple random walk and asymptotic estimates for loop-erased random walk, which are of independent interest.
Publié le : 2010-11-15
Classification:  Random walk in random environment,  Random walk trace,  Heat kernel estimates,  Cut time,  Loop erased random walk,  82C41 
@article{1288878335,
     author = {Shiraishi, Daisuke},
     title = {Heat kernel for random walk trace on $\mathbb{Z}$<sup>3</sup> and $\mathbb{Z}$<sup>4</sup>},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {46},
     number = {1},
     year = {2010},
     pages = { 1001-1024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1288878335}
}

Shiraishi, Daisuke. Heat kernel for random walk trace on ℤ3 and ℤ4. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp.  1001-1024. http://gdmltest.u-ga.fr/item/1288878335/