% Frozen bibliography for the present publication. @article{AmorimHaydnVaienti2025, author = {Amorim, Lucas and Haydn, Nicolai and Vaienti, Sandro}, title = {{Compound Poisson distributions for random dynamical systems using probabilistic approximations}}, journaltitle = {Stochastic Processes and their Applications}, volume = {179}, eid = {104511}, year = {2025}, doi = {10.1016/j.spa.2024.104511}, eprinttype = {arxiv}, eprint = {2402.02759} } @article{ArratiaGoldsteinGordon1989, author = {Arratia, Richard and Goldstein, Larry and Gordon, Louis}, title = {{Two moments suffice for {Poisson} approximations: The {Chen--Stein} method}}, volume = {17}, number = {1}, pages = {9--25}, year = {1989}, doi = {10.1214/aop/1176991491}, journaltitle = {Annals of Probability} } @article{ArratiaGoldsteinGordon1990, author = {Arratia, Richard and Goldstein, Larry and Gordon, Louis}, title = {{Poisson approximation and the {Chen--Stein} method}}, volume = {5}, number = {4}, pages = {403--424}, year = {1990}, doi = {10.1214/ss/1177012015}, journaltitle = {Statistical Science} } @article{AtnipFroylandGonzalezTokmanVaienti2025, author = {J.~Atnip and G.~Froyland and C.~Gonz\'alez-Tokman and S.~Vaienti}, title = {{Compound Poisson statistics for dynamical systems via spectral perturbation}}, doi = {10.1088/1361-6544/adfa62}, eprint = {2308.10798}, eprinttype = {arxiv}, year = {2025}, volume = {38}, journaltitle = {Nonlinearity}, eid = {085023} } @article{BacryMuzy2016, author = {E.~Bacry and J.-F.~Muzy}, title = {{First- and second-order statistics characterization of Hawkes processes and non-parametric estimation}}, doi = {10.1109/TIT.2016.2533397}, eprint = {1401.0903}, eprinttype = {arxiv}, year = {2016}, volume = {62}, journaltitle = {IEEE Transactions on Information Theory}, number = {4}, pages = {2184--2202} } @article{DengMoody2009, author = {X.~Deng and R.~V.~Moody}, title = {{How model sets can be determined by their two-point and three-point correlations}}, doi = {10.1007/s10955-009-9742-0}, eprint = {0901.4381}, eprinttype = {arxiv}, year = {2009}, volume = {135}, journaltitle = {Journal of Statistical Physics}, pages = {621--637} } @article{Dohmen2000, author = {K.~Dohmen}, title = {{Improved inclusion-exclusion identities via closure operators}}, doi = {10.46298/dmtcs.275}, year = {2000}, volume = {4}, journaltitle = {Discrete Mathematics \& Theoretical Computer Science}, number = {1}, pages = {61--66} } @article{GrimmBaake2008, author = {U.~Grimm and M.~Baake}, title = {{Homometric point sets and inverse problems}}, doi = {10.1524/zkri.2008.1043}, eprint = {0808.0094}, eprinttype = {arxiv}, year = {2008}, volume = {223}, journaltitle = {Zeitschrift f\"ur Kristallographie}, pages = {777--781} } @article{HawkesOakes1974, author = {A.~G.~Hawkes and D.~Oakes}, title = {{A cluster process representation of a self-exciting process}}, doi = {10.2307/3212693}, year = {1974}, volume = {11}, journaltitle = {Journal of Applied Probability}, number = {3}, pages = {493--503} } @article{HaydnVaienti2009, author = {Haydn, Nicolai and Vaienti, Sandro}, title = {{The compound {Poisson} distribution and return times in dynamical systems}}, volume = {144}, pages = {517--542}, year = {2009}, doi = {10.1007/s00440-008-0153-y}, journaltitle = {Probability Theory and Related Fields}, eprint = {0804.1032}, eprinttype = {arxiv} } @article{HildebrandTenenbaum1993, author = {A.~Hildebrand and G.~Tenenbaum}, title = {{Integers without large prime factors}}, year = {1993}, volume = {5}, journaltitle = {Journal de th\'eorie des nombres de Bordeaux}, number = {2}, pages = {411--484}, url = {https://www.numdam.org/item/JTNB_1993__5_2_411_0/}, doi = {10.5802/jtnb.101} } @article{Hunter1976, author = {D.~Hunter}, title = {{An upper bound for the probability of a union}}, doi = {10.2307/3212481}, year = {1976}, volume = {13}, journaltitle = {Journal of Applied Probability}, number = {3}, pages = {597--603} } @article{KempKemp1965, author = {C.~D.~Kemp and A.~W.~Kemp}, title = {{Some properties of the `Hermite' distribution}}, doi = {10.1093/biomet/52.3-4.381}, year = {1965}, volume = {52}, journaltitle = {Biometrika}, number = {3--4}, pages = {381--394} } @article{Kerscher2001, author = {M.~Kerscher}, title = {{Constructing, characterizing, and simulating Gaussian and higher-order point distributions}}, doi = {10.1103/PhysRevE.64.056109}, eprint = {astro-ph/0102153}, eprinttype = {arxiv}, year = {2001}, volume = {64}, journaltitle = {Physical Review E}, eid = {056109} } @article{KiferRapaport2014, author = {Kifer, Yuri and Rapaport, Ariel}, title = {{{Poisson} and compound {Poisson} approximations in conventional and nonconventional setups}}, volume = {160}, pages = {797--831}, year = {2014}, doi = {10.1007/s00440-013-0541-9}, journaltitle = {Probability Theory and Related Fields}, eprint = {1211.5238}, eprinttype = {arxiv} } @incollection{Last2016, author = {Last, Günter}, title = {{Stochastic analysis for Poisson processes}}, eprint = {1405.4416}, eprinttype = {arxiv}, year = {2016}, booktitle = {Stochastic Analysis for Poisson Point Processes}, publisher = {Springer}, pages = {1--36}, doi = {10.1007/978-3-319-05233-5_1}, editor = {Peccati, Giovanni and Reitzner, Matthias}, series = {Bocconi \& Springer Series}, volume = {7} } @book{LastPenrosePoissonProcess, author = {Last, Günter and Penrose, Mathew}, title = {{Lectures on the Poisson Process}}, doi = {10.1017/9781316104477}, year = {2017}, publisher = {Cambridge University Press}, series = {Institute of Mathematical Statistics Textbooks}, number = {7}, url = {https://stoch.math.kit.edu/img/Last/lastpenrose2017.pdf} } @article{MollerSyversveenWaagepetersen1998, author = {J.~M\o ller and A.~R.~Syversveen and R.~P.~Waagepetersen}, title = {{Log Gaussian Cox processes}}, doi = {10.1111/1467-9469.00115}, year = {1998}, volume = {25}, journaltitle = {Scandinavian Journal of Statistics}, number = {3}, pages = {451--482} } @article{NaimanWynn1992, author = {D.~Q.~Naiman and H.~P.~Wynn}, title = {{Inclusion-exclusion-Bonferroni identities and inequalities for discrete tube-like problems via Euler characteristics}}, doi = {10.1214/aos/1176348512}, year = {1992}, volume = {20}, journaltitle = {Annals of Statistics}, number = {1}, pages = {43--76} } @article{NaimanWynn1997, author = {D.~Q.~Naiman and H.~P.~Wynn}, title = {{Abstract tubes, improved inclusion-exclusion identities and inequalities and importance sampling}}, doi = {10.1214/aos/1069362380}, year = {1997}, volume = {25}, journaltitle = {Annals of Statistics}, number = {5}, pages = {1954--1983} } @article{Najnudel2020, author = {Najnudel, Joseph}, title = {{On consecutive values of random completely multiplicative functions}}, volume = {25}, year = {2020}, doi = {10.1214/20-EJP456}, journaltitle = {Electronic Journal of Probability}, eprint = {1702.01470}, eprinttype = {arxiv}, eid = {59} } @article{Newman1970, author = {D.~S.~Newman}, title = {{A new family of point processes which are characterized by their second moment properties}}, doi = {10.2307/3211969}, year = {1970}, volume = {7}, journaltitle = {Journal of Applied Probability}, number = {2}, pages = {338--358} } @article{PeneSaussol2020, author = {P{\`e}ne, Fran{\c c}oise and Saussol, Beno{\^i}t}, title = {{Spatio-temporal {Poisson} processes for visits to small sets}}, volume = {240}, number = {2}, pages = {625--665}, year = {2020}, doi = {10.1007/s11856-020-2074-0}, journaltitle = {Israel Journal of Mathematics}, eprint = {1803.06865}, eprinttype = {arxiv} } @article{Rapaport2016, author = {Rapaport, Ariel}, title = {{Compound {Poisson} statistics for multiple returns in shrinking cylinders for mixing processes}}, volume = {36}, number = {5}, pages = {1616--1643}, year = {2016}, doi = {10.1017/etds.2014.139}, journaltitle = {Ergodic Theory and Dynamical Systems}, eprint = {1404.3516}, eprinttype = {arxiv} } @article{ReinertSchbath1998, author = {Reinert, Gesine and Schbath, Sophie}, title = {{Compound {Poisson} and {Poisson} process approximations for occurrences of multiple words in {Markov} chains}}, volume = {5}, number = {2}, pages = {223--253}, year = {1998}, doi = {10.1089/cmb.1998.5.223}, journaltitle = {Journal of Computational Biology} } @article{SchuhmacherXia2008, author = {D.~Schuhmacher and A.~Xia}, title = {{A new metric between distributions of point processes}}, eprint = {0708.2777}, eprinttype = {arxiv}, year = {2008}, volume = {40}, journaltitle = {Advances in Applied Probability}, pages = {651--672}, number = {3}, doi = {10.1239/aap/1222868180} } @article{Worsley1982, author = {K.~J.~Worsley}, title = {{An improved Bonferroni inequality and applications}}, doi = {10.1093/biomet/69.2.297}, year = {1982}, volume = {69}, journaltitle = {Biometrika}, number = {2}, pages = {297--302} } @unpublished{PoulyLongRuns, author = {Pouly, Brice}, title = {{Long runs and rare patterns of a random completely multiplicative function}}, date = {2026-09-21}, note = {Preprint, Version 3. Zenodo. With technical companion}, doi = {10.5281/zenodo.22872154} } @unpublished{PoulyLatticePoissonFlows, author = {Pouly, Brice}, title = {{Records, scale flows, and Gaussian limits from lattice Poisson fields}}, date = {2026-09-21}, note = {Preprint, Version 2. Zenodo. With technical companion}, doi = {10.5281/zenodo.22876520} } @unpublished{PoulyArithmeticClusters, author = {Pouly, Brice}, title = {{Poisson laws and arithmetic clusters for rare multiplicative patterns}}, date = {2026-09-21}, note = {Preprint, Version 1. Zenodo}, doi = {10.5281/zenodo.22877400} }