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

2006
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Electronic Journal of Probability
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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

doi:10.1214/ejp.v11-330
fatcat:t6n4dnqgk5f3xdbwdvjp42v6wi