Point processes and topological algebra
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.. module:: Homology
   :synopsis: Point processes, topological algebra and applications to wireless systems

My `list of publications <https://hal.archives-ouvertes.fr/search/index/?q=decreusefond&submit=&keyword_t=Homology&sort=producedDate_tdate+desc>`_ about topological algebra
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The latest publications
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- Read more about :ref:`Optimal transport between determinantal point processes and application to fast simulation <simulationGinibre>`.


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.. _simulationGinibre:

Optimal transport between determinantal point processes and application to fast simulation
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The simulation of determinantal point processes by the classical algorithm introduced by `Hough et al. <https://projecteuclid.org/journals/probability-surveys/volume-3/issue-none/Determinantal-Processes-and-Independence/10.1214/154957806000000078.full>`_  suffer from two flaws : a large number of rejections and a huge number of computations to obtain the densities. For radially symmetric determinantal point processes, like the :math:`\beta`-Ginibre or Bergman processes, we show how to overcome these two difficulties and obtain  a fast approximate simulation. 
The errors are evaluated in Wasserstein distances and shown to be asymptotically evanescent. The code is freely available at `<https://gitlab.inria.fr/gmoro/point_process>`_


.. note::
   * `Version HAL <https://hal.archives-ouvertes.fr/hal-02984323>`_

.. parsed-literal::
   @article{decreusefond_moroz_2021,
  author = {Laurent Decreusefond and Guillaume Moroz},
  title = {Optimal transport between determinantal point processes and application to fast simulation},
  journal = {Modern Stochastics: Theory and Applications},
  volume = {8},
  number = {2},
  year = {2021},
  pages = {209--237},
  doi = {10.15559/21-VMSTA180},
  issn = {2351-6046}}