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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageUnknown
Title of host publicationQP-PQ Quantum Probability and White Noise Analysis
Pages55-70
Publication statusPublished - 1 Jan 2010
Event29th Conference on Quantum Probability and Related Topics -
Duration: 1 Jan 2010 → …

Conference

Conference29th Conference on Quantum Probability and Related Topics
Period1/01/10 → …

Keywords

    Cite this

    @inproceedings{3f99f7ab218647dda6e819596354e5e7,
    title = "The Gibbs Conditioning Principle for White Noise Distributions: interacting and non-interacting cases",
    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.",
    keywords = "Positive White Noise distributions, Large Deviation Principle, Gibbs measure",
    author = "Marques, {Maria Fernanda de Almeida Cipriano Salvador}",
    year = "2010",
    month = "1",
    day = "1",
    language = "Unknown",
    isbn = "978-981-4295-42-0",
    pages = "55--70",
    booktitle = "QP-PQ Quantum Probability and White Noise Analysis",

    }

    Marques, MFDACS 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, 29th Conference on Quantum Probability and Related Topics, 1/01/10.

    . / Marques, Maria Fernanda de Almeida Cipriano Salvador.

    QP-PQ Quantum Probability and White Noise Analysis. 2010. p. 55-70.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    TY - GEN

    T1 - The Gibbs Conditioning Principle for White Noise Distributions: interacting and non-interacting cases

    AU - Marques, Maria Fernanda de Almeida Cipriano Salvador

    PY - 2010/1/1

    Y1 - 2010/1/1

    N2 - 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.

    AB - 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.

    KW - Positive White Noise distributions

    KW - Large Deviation Principle

    KW - Gibbs measure

    M3 - Conference contribution

    SN - 978-981-4295-42-0

    SP - 55

    EP - 70

    BT - QP-PQ Quantum Probability and White Noise Analysis

    ER -