We compute the average shape of trajectories of some one-dimensional stochastic processes x t in the t , x
plane during an excursion, i.e., between two successive returns to a reference value, finding that it obeys a
scaling form. For uncorrelated random walks the average shape is semicircular, independent from the single
increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy
flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys
scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations
induces nontrivial asymmetric shapes, which are studied numerically.
%0 Journal Article
%1 colaiori:041105
%A Colaiori, Francesca
%A Baldassarri, Andrea
%A Castellano, Claudio
%D 2004
%I APS
%J Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
%K averageshape randomprocesses barkhausen myown levy 2004 randomwalk physics fluctuations pre
%N 4
%P 041105
%T Average trajectory of returning walks
%U http://link.aps.org/abstract/PRE/v69/e041105
%V 69
%X We compute the average shape of trajectories of some one-dimensional stochastic processes x t in the t , x
plane during an excursion, i.e., between two successive returns to a reference value, finding that it obeys a
scaling form. For uncorrelated random walks the average shape is semicircular, independent from the single
increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy
flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys
scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations
induces nontrivial asymmetric shapes, which are studied numerically.
@article{colaiori:041105,
abstract = { We compute the average shape of trajectories of some one-dimensional stochastic processes x t in the t , x
plane during an excursion, i.e., between two successive returns to a reference value, finding that it obeys a
scaling form. For uncorrelated random walks the average shape is semicircular, independent from the single
increments distribution, as long as it is symmetric. Such universality extends to biased random walks and Levy
flights, with the exception of a particular class of biased Levy flights. Adding a linear damping term destroys
scaling and leads asymptotically to flat excursions. The introduction of short and long ranged noise correlations
induces nontrivial asymmetric shapes, which are studied numerically.
},
added-at = {2006-10-17T19:50:58.000+0200},
author = {Colaiori, Francesca and Baldassarri, Andrea and Castellano, Claudio},
biburl = {https://www.bibsonomy.org/bibtex/2f42de8c8c7d7b2ac2202a3f377ca38f1/andreab},
eid = {041105},
interhash = {0a89e8058d0fe1fc45ea37e20834e89d},
intrahash = {f42de8c8c7d7b2ac2202a3f377ca38f1},
journal = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)},
keywords = {averageshape randomprocesses barkhausen myown levy 2004 randomwalk physics fluctuations pre},
number = 4,
numpages = {11},
pages = 041105,
publisher = {APS},
timestamp = {2006-10-17T19:50:58.000+0200},
title = {Average trajectory of returning walks},
url = {http://link.aps.org/abstract/PRE/v69/e041105},
volume = 69,
year = 2004
}