The spread of a catalytic branching random walk
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, p. 327-351

We consider a catalytic branching random walk on that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position M n : For some constant α, M n nα almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for M n -αn as n goes to infinity.

Nous considérons une marche aléatoire branchant catalytique sur qui ne branche qu’à l’origine. Dans le cas surcritique, nous établissons une loi des grands nombres pour la position maximale M n : Il existe une constante α explicite telle que M n nα presque sûrement sur l’ensemble des trajectoires pour lesquelles l’origine est visitée une infinité de fois. Ensuite, nous déterminons toutes les lois limites possibles, lorsque n+, pour la suite M n -αn.

DOI : https://doi.org/10.1214/12-AIHP529
Classification:  60K37
Keywords: branching processes, catalytic branching random walk
@article{AIHPB_2014__50_2_327_0,
     author = {Carmona, Philippe and Hu, Yueyun},
     title = {The spread of a catalytic branching random walk},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {2},
     year = {2014},
     pages = {327-351},
     doi = {10.1214/12-AIHP529},
     zbl = {1291.60208},
     mrnumber = {3189074},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_2_327_0}
}
Carmona, Philippe; Hu, Yueyun. The spread of a catalytic branching random walk. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, pp. 327-351. doi : 10.1214/12-AIHP529. http://www.numdam.org/item/AIHPB_2014__50_2_327_0/

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