Superdiffusivity for brownian motion in a poissonian potential with long range correlation II: Upper bound on the volume exponent

Hubert Lacoin

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 4, page 1029-1048
  • ISSN: 0246-0203

Abstract

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This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here that for both point-to-point and point-to-plane model the volume exponent (the exponent associated to transversal fluctuation of the trajectories) ξ is strictly less than 1 and give an explicit upper bound that depends on the parameters of the problem. In some specific cases, this upper bound matches the lower bound proved in the first part of this work and we get the exact value of the volume exponent.

How to cite

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Lacoin, Hubert. "Superdiffusivity for brownian motion in a poissonian potential with long range correlation II: Upper bound on the volume exponent." Annales de l'I.H.P. Probabilités et statistiques 48.4 (2012): 1029-1048. <http://eudml.org/doc/271959>.

@article{Lacoin2012,
abstract = {This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here that for both point-to-point and point-to-plane model the volume exponent (the exponent associated to transversal fluctuation of the trajectories) $\xi $ is strictly less than $1$ and give an explicit upper bound that depends on the parameters of the problem. In some specific cases, this upper bound matches the lower bound proved in the first part of this work and we get the exact value of the volume exponent.},
author = {Lacoin, Hubert},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stretched polymer; quenched disorder; superdiffusivity; brownian motion; poissonian obstacles; correlation; Stretched polymer; Brownian motion; Poissonian obstacles},
language = {eng},
number = {4},
pages = {1029-1048},
publisher = {Gauthier-Villars},
title = {Superdiffusivity for brownian motion in a poissonian potential with long range correlation II: Upper bound on the volume exponent},
url = {http://eudml.org/doc/271959},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Lacoin, Hubert
TI - Superdiffusivity for brownian motion in a poissonian potential with long range correlation II: Upper bound on the volume exponent
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 4
SP - 1029
EP - 1048
AB - This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here that for both point-to-point and point-to-plane model the volume exponent (the exponent associated to transversal fluctuation of the trajectories) $\xi $ is strictly less than $1$ and give an explicit upper bound that depends on the parameters of the problem. In some specific cases, this upper bound matches the lower bound proved in the first part of this work and we get the exact value of the volume exponent.
LA - eng
KW - stretched polymer; quenched disorder; superdiffusivity; brownian motion; poissonian obstacles; correlation; Stretched polymer; Brownian motion; Poissonian obstacles
UR - http://eudml.org/doc/271959
ER -

References

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  8. [8] A. S. Sznitman. Shape theorem, Lyapounov exponents and large deviation for Brownian motion in Poissonian potential. Comm. Pure Appl. Math. 47 (1994) 1655–1688. Zbl0814.60022MR1303223
  9. [9] A. S. Sznitman. Distance fluctuations and Lyapounov exponents. Ann. Probab.24 (1996) 1507–1530. Zbl0871.60088MR1411504
  10. [10] A. S. Sznitman. Brownian Motion, Obstacles and Random Media. Springer Monographs in Mathematics. Springer, Berlin, 1998. Zbl0815.60077MR1717054
  11. [11] M. Wütrich. Superdiffusive behavior of two-dimensional Brownian motion in a Poissonian potential. Ann. Probab.26 (1998) 1000–1015. Zbl0935.60099MR1634412
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