Yuri Kifer, Ariel Rapaport
Abstract
Open-access reader
We show that for all $ψ$-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe completely the asymptotic behavior of these distributions.
OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
We show that for all $ψ$-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe completely the asymptotic behavior of these distributions.
Key concepts: Poisson distribution, Compound Poisson distribution, Statistical physics, Zero-inflated model, Compound Poisson process, Mixing (physics), Physics, Poisson regression