%0 Journal Article %1 Mueller2014Phenomenological %A Mueller, A. H. %A Munier, S. %D 2014 %J Physical Review E %K teaching %N 4 %R 10.1103/physreve.90.042143 %T Phenomenological picture of fluctuations in branching random walks %U http://dx.doi.org/10.1103/physreve.90.042143 %V 90 %X We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the \$1/t\$ correction to the average position of the rightmost particle of a branching random walk for large times \$t1\$, computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of branching random walk.

@article{Mueller2014Phenomenological, abstract = {We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the \$1/\sqrt{t}\$ correction to the average position of the rightmost particle of a branching random walk for large times \$t\gg 1\$, computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of branching random walk.}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {Mueller, A. H. and Munier, S.}, biburl = {https://www.bibsonomy.org/bibtex/20a8434613e58dfea7a904473f39afb7d/cmcneile}, citeulike-article-id = {13528817}, citeulike-linkout-0 = {http://arxiv.org/abs/1404.5500}, citeulike-linkout-1 = {http://arxiv.org/pdf/1404.5500}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/physreve.90.042143}, day = 22, doi = {10.1103/physreve.90.042143}, eprint = {1404.5500}, interhash = {fdb38dae564250c1d89a84bc61533f07}, intrahash = {0a8434613e58dfea7a904473f39afb7d}, issn = {1539-3755}, journal = {Physical Review E}, keywords = {teaching}, month = oct, number = 4, posted-at = {2015-02-26 17:16:57}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{Phenomenological picture of fluctuations in branching random walks}}, url = {http://dx.doi.org/10.1103/physreve.90.042143}, volume = 90, year = 2014 }