### Abstract

Let Y = (Y-i)(i is an element of N) be a sequence of i. i. d. random variables taking values in the dual of a real nuclear frechet space. We denote by L-n(Y) the empirical measure associated with these variables. In this paper we study the limit law of (Y-1,..., Y-k) under the constraint E-U (L-n(Y)) is an element of D where D is a measurable subset of R, and E-U is the energy functional associated to a fixed positive test function U. For some particular choices of the functional E-U, we consider non interacting case, i.e., when the particles Y-1,..., Y-k do not affect each other and the case where interaction is present. In both cases, we show that the conditional law of Y-1 converges, as n -> infinity, to a Gibbs measure.

Original language | Unknown |
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Title of host publication | QP-PQ Quantum Probability and White Noise Analysis |

Pages | 55-70 |

Publication status | Published - 1 Jan 2010 |

Event | 29th Conference on Quantum Probability and Related Topics - Duration: 1 Jan 2010 → … |

### Conference

Conference | 29th Conference on Quantum Probability and Related Topics |
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Period | 1/01/10 → … |

## Cite this

Marques, M. F. D. A. C. S. (2010).

The Gibbs Conditioning Principle for White Noise Distributions: interacting and non-interacting cases

. In *QP-PQ Quantum Probability and White Noise Analysis*(pp. 55-70)