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Large systems of path-repellent Brownian motions in a trap at positive temperature

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1.	Title	Title of document	Large systems of path-repellent Brownian motions in a trap at positive temperature
2.	Creator	Author's name, affiliation, country	Stefan Adams; Max Planck Institute for Mathematics in the Sciences
2.	Creator	Author's name, affiliation, country	Jean-Bernard Bru; Johannes-Gutenberg-Universitat Mainz
2.	Creator	Author's name, affiliation, country	Wolfgang Koenig; Universitat Leipzig
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Interacting Brownian motions; Brownian intersection local times; large deviations; occupation measure; Gross-Pitaevskii formula
3.	Subject	Subject classification	60F10; 60J65; 82B10; 82B26
4.	Description	Abstract	We study a model of $ N $ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from escaping to infinity, and a pair-interaction Hamiltonian, which imposes a repellency of the $N$ paths. In fact, this interaction is an $N$-dependent regularisation of the Brownian intersection local times, an object which is of independent interest in the theory of stochastic processes. The time horizon (interpreted as the inverse temperature) is kept fixed. We analyse the model for diverging number of Brownian motions in terms of a large deviation principle. The resulting variational formula is the positive-temperature analogue of the well-known Gross-Pitaevskii formula, which approximates the ground state of a certain dilute large quantum system; the kinetic energy term of that formula is replaced by a probabilistic energy functional. This study is a continuation of the analysis in [ABK06] where we considered the limit of diverging time (i.e., the zero-temperature limit) with fixed number of Brownian motions, followed by the limit for diverging number of motions.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	This work was partially supported by DFG grant AD 194/1-1
7.	Date	(YYYY-MM-DD)	2006-06-29
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/330
10.	Identifier	Digital Object Identifier	10.1214/EJP.v11-330
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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