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Poisson Ensembles of Loops of One-Dimensional Diffusions
 
Titus Lupu Sorbonne Université, Paris, France
A publication of the Société Mathématique de France
Poisson Ensembles of Loops of One-Dimensional Diffusions
Softcover ISBN:  978-2-85629-891-6
Product Code:  SMFMEM/158
List Price: $48.00
AMS Member Price: $38.40
Please note AMS points can not be used for this product
Poisson Ensembles of Loops of One-Dimensional Diffusions
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Poisson Ensembles of Loops of One-Dimensional Diffusions
Titus Lupu Sorbonne Université, Paris, France
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-891-6
Product Code:  SMFMEM/158
List Price: $48.00
AMS Member Price: $38.40
Please note AMS points can not be used for this product
  • Book Details
     
     
    Mémoires de la Société Mathématique de France
    Volume: 1582018; 162 pp
    MSC: Primary 60

    There is a natural measure on loops (time-parametrized trajectories that, in the end, return to the origin) which one can associate to a wide class of Markov processes. The Poisson ensembles of Markov loops are Poisson point processes with intensity proportional to these measures. In wide generality, these Poisson ensembles of Markov loops are related, at intensity parameter 1/2, to the Gaussian free field, and at intensity parameter 1, to the loops done by a Markovian sample path.

    Here, the author studies the specific case when the Markov process is a one-dimensional diffusion. After a detailed description of the measure, the author studies the Poisson point processes of loops, their occupation fields, and explains how to sample these Poisson ensembles of loops out of diffusion sample path perturbed at their successive minima.

    Finally, the author introduces a couple of interwoven determinantal point processes on the line, which is a dual through Wilson's algorithm of Poisson ensembles of loops, and studies the properties of these determinantal point processes.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1582018; 162 pp
MSC: Primary 60

There is a natural measure on loops (time-parametrized trajectories that, in the end, return to the origin) which one can associate to a wide class of Markov processes. The Poisson ensembles of Markov loops are Poisson point processes with intensity proportional to these measures. In wide generality, these Poisson ensembles of Markov loops are related, at intensity parameter 1/2, to the Gaussian free field, and at intensity parameter 1, to the loops done by a Markovian sample path.

Here, the author studies the specific case when the Markov process is a one-dimensional diffusion. After a detailed description of the measure, the author studies the Poisson point processes of loops, their occupation fields, and explains how to sample these Poisson ensembles of loops out of diffusion sample path perturbed at their successive minima.

Finally, the author introduces a couple of interwoven determinantal point processes on the line, which is a dual through Wilson's algorithm of Poisson ensembles of loops, and studies the properties of these determinantal point processes.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.