An infinite point process (= an infinite discrete random set of points) is said to be hyperuniform along an exhaustion by bounded sets if the ratio (variance of the number of points)/(expectation of the number of points) goes to zero along the exhaustion. In this talk, I will present geometric methods that allow to derive hyperuniformity or nonhyperuniformity for determinantal point processes that are invariant by isometries. In particular, we obtain that translation invariant determinantal point processes on $R^d$ are hyperuniform along any exhaustion by open sets, while determinantal point processes on Gromov hyperbolic metric spaces  which include the known examples on Cayley trees and standard real or complex hyperbolic spaces $H^d$  are never hyperuniform. If time permits, I will discuss applications to accumulated spectrograms together with some analogy with quantum ergodicity.
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Hyperuniform determinantal point processes
Research Group:
Speaker:
Pierre Karim Emile Lazag
Institution:
SISSA
Schedule:
Wednesday, November 22, 2023  16:00 to 17:00
Location:
A136
Location:
SISSA Main Building
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