
Softcover ISBN: | 978-2-85629-891-6 |
Product Code: | SMFMEM/158 |
List Price: | $48.00 |
AMS Member Price: | $38.40 |

Softcover ISBN: | 978-2-85629-891-6 |
Product Code: | SMFMEM/158 |
List Price: | $48.00 |
AMS Member Price: | $38.40 |
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Book DetailsMémoires de la Société Mathématique de FranceVolume: 158; 2018; 162 ppMSC: 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.
ReadershipGraduate students and research mathematicians.
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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.
Graduate students and research mathematicians.