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UID:925@lincs.fr
DTSTART;TZID=Europe/Paris:20251008T140000
DTEND;TZID=Europe/Paris:20251008T150000
DTSTAMP:20251020T101843Z
URL:https://www.lincs.fr/events/estimating-the-hyperuniformity-exponent-of
 -point-processes/
SUMMARY:Estimating the hyperuniformity exponent of point processes
DESCRIPTION:A joint work with G. Mastrilli\, B. Blaszczyszyn\, F.
 Lavancier\n\nHyperuniformity characterizes random spatial structures whose
 large-scale variance grows more slowly than that of Poisson processes.
 First introduced in statistical physics by Torquato and Stillinger [1]\,
 hyperuniform systems have attracted considerable attention due to their
 intermediate nature between perfect crystals\, liquids\, and glasses\, and
 appears in a wide range of applications\, from DNA organization and immune
 system dynamics to photoreceptor arrangements\, urban planning\, and
 cosmology.\nDetecting and quantifying hyperuniformity is essential across
 these diverse fields. Yet\, statistical testing for hyperuniformity has
 only recently begun to develop. In joint work [2]\, we address the problem
 of estimating the “strength” of hyperuniformity—formally\, the
 exponent governing the decay of the spectral density near zero
 frequency—in a class of stationary point\nprocesses in Euclidean space.
 The key mathematical idea is that the variance of linear statistics\,
 defined using smooth\, rapidly decaying test functions\, grows in a way
 that explicitly reflects this exponent. Using a multivariate central limit
 theorem for a family of such statistics\, constructed from orthogonal
 functions at multiple scales (e.g.\, wavelets)\, we derive
 an\nasymptotically consistent estimator of the strength of hyperuniformity.
 This estimator can be computed from a single realization of the point
 process and comes with explicit confidence intervals. We validate this
 approach through simulations of various point process models and
 demonstrate its applicability on real data.\n\nBibliography\n[1] Torquato\,
 S. and Stillinger\, F. H. (2003). Local density fluctuations\,
 hyperuniformity\, and order metrics. Physical Review E 68 041113.\n[2]
 Mastrilli\, G.\, B laszczyszyn\, B. and Lavancier\, F. (2024) Estimating
 the hyperuniformity exponent of point processes arXiv:2407.16797.
CATEGORIES:Seminars,Youtube
LOCATION:Amphi 7\, 19 Place Marguerite Perey\, Palaiseau\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=19 Place Marguerite Perey\,
 Palaiseau\, France;X-APPLE-RADIUS=100;X-TITLE=Amphi 7:geo:0,0
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TZID:Europe/Paris
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DTSTART:20250330T030000
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