%0 Journal Article %1 birkner2013directed %A Birkner, Matthias %A Černý, Jiří %A Depperschmidt, Andrej %A Gantert, Nina %D 2013 %I Institute of Mathematical Statistics %J Electronic Journal of Probability %K ancestral_process lineage_movement percolation %N none %R 10.1214/ejp.v18-2302 %T Directed random walk on the backbone of an oriented percolation cluster %U https://doi.org/10.1214%2Fejp.v18-2302 %V 18 %X We consider a directed random walk on the backbone of the infinite cluster gener- ated by supercritical oriented percolation, or equivalently the space-time embedding of the “ancestral lineage” of an individual in the stationary discrete-time contact pro- cess. We prove a law of large numbers and an annealed central limit theorem (i.e., averaged over the realisations of the cluster) using a regeneration approach. Fur- thermore, we obtain a quenched central limit theorem (i.e. for almost any realisation of the cluster) via an analysis of joint renewals of two independent walks on the same cluster.

@article{birkner2013directed, abstract = {We consider a directed random walk on the backbone of the infinite cluster gener- ated by supercritical oriented percolation, or equivalently the space-time embedding of the “ancestral lineage” of an individual in the stationary discrete-time contact pro- cess. We prove a law of large numbers and an annealed central limit theorem (i.e., averaged over the realisations of the cluster) using a regeneration approach. Fur- thermore, we obtain a quenched central limit theorem (i.e. for almost any realisation of the cluster) via an analysis of joint renewals of two independent walks on the same cluster.}, added-at = {2021-06-30T17:50:18.000+0200}, author = {Birkner, Matthias and Černý, Jiří and Depperschmidt, Andrej and Gantert, Nina}, biburl = {https://www.bibsonomy.org/bibtex/23abd6aaecd9ab3c113cb297da3b6ab66/peter.ralph}, doi = {10.1214/ejp.v18-2302}, interhash = {bab5986e6bcd464f33264e337460102f}, intrahash = {3abd6aaecd9ab3c113cb297da3b6ab66}, journal = {Electronic Journal of Probability}, keywords = {ancestral_process lineage_movement percolation}, month = jan, number = {none}, publisher = {Institute of Mathematical Statistics}, timestamp = {2021-06-30T17:50:18.000+0200}, title = {Directed random walk on the backbone of an oriented percolation cluster}, url = {https://doi.org/10.1214%2Fejp.v18-2302}, volume = 18, year = 2013 }