---
_id: '8515'
abstract:
- lang: eng
text: "We consider the evolution of a set carried by a space periodic incompressible
stochastic flow in a Euclidean space. We\r\nreport on three main results obtained
in [8, 9, 10] concerning long time behaviour for a typical realization of the
stochastic flow. First, at time t most of the particles are at a distance of order
√t away from the origin. Moreover, we prove a Central Limit Theorem for the evolution
of a measure carried by the flow, which holds for almost every realization of
the flow. Second, we show the existence of a zero measure full Hausdorff dimension
set of points, which\r\nescape to infinity at a linear rate. Third, in the 2-dimensional
case, we study the set of points visited by the original set by time t. Such a
set, when scaled down by the factor of t, has a limiting non random shape."
article_processing_charge: No
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: D.
full_name: DOLGOPYAT, D.
last_name: DOLGOPYAT
- first_name: L.
full_name: KORALOV, L.
last_name: KORALOV
citation:
ama: 'Kaloshin V, DOLGOPYAT D, KORALOV L. Long time behaviour of periodic stochastic
flows. In: *XIVth International Congress on Mathematical Physics*. World
Scientific; 2006:290-295. doi:10.1142/9789812704016_0026'
apa: 'Kaloshin, V., DOLGOPYAT, D., & KORALOV, L. (2006). Long time behaviour
of periodic stochastic flows. In *XIVth International Congress on Mathematical
Physics* (pp. 290–295). Lisbon, Portugal: World Scientific. https://doi.org/10.1142/9789812704016_0026'
chicago: Kaloshin, Vadim, D. DOLGOPYAT, and L. KORALOV. “Long Time Behaviour of
Periodic Stochastic Flows.” In *XIVth International Congress on Mathematical
Physics*, 290–95. World Scientific, 2006. https://doi.org/10.1142/9789812704016_0026.
ieee: V. Kaloshin, D. DOLGOPYAT, and L. KORALOV, “Long time behaviour of periodic
stochastic flows,” in *XIVth International Congress on Mathematical Physics*,
Lisbon, Portugal, 2006, pp. 290–295.
ista: Kaloshin V, DOLGOPYAT D, KORALOV L. 2006. Long time behaviour of periodic
stochastic flows. XIVth International Congress on Mathematical Physics. International
Congress on Mathematical Physics, 290–295.
mla: Kaloshin, Vadim, et al. “Long Time Behaviour of Periodic Stochastic Flows.”
*XIVth International Congress on Mathematical Physics*, World Scientific,
2006, pp. 290–95, doi:10.1142/9789812704016_0026.
short: V. Kaloshin, D. DOLGOPYAT, L. KORALOV, in:, XIVth International Congress
on Mathematical Physics, World Scientific, 2006, pp. 290–295.
conference:
end_date: 2003-08-02
location: Lisbon, Portugal
name: International Congress on Mathematical Physics
start_date: 2003-07-28
date_created: 2020-09-18T10:48:59Z
date_published: 2006-03-01T00:00:00Z
date_updated: 2021-01-12T08:19:49Z
day: '01'
doi: 10.1142/9789812704016_0026
extern: '1'
language:
- iso: eng
month: '03'
oa_version: None
page: 290-295
publication: XIVth International Congress on Mathematical Physics
publication_identifier:
isbn:
- '9789812562012'
- '9789812704016'
publication_status: published
publisher: World Scientific
quality_controlled: '1'
status: public
title: Long time behaviour of periodic stochastic flows
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2006'
...