% Frozen bibliography for this edition; local numbering is generated by Biber.

@article{AlvarezBecherMereb2023,
  author = {N. \'Alvarez and V. Becher and M. Mereb},
  title = {{Poisson generic sequences}},
  doi = {10.1093/imrn/rnac234},
  eprint = {2202.01632},
  eprinttype = {arxiv},
  year = {2023},
  volume = {2023},
  journaltitle = {International Mathematics Research Notices},
  number = {24},
  pages = {20970--20987}
}

@article{AlvarezEtAlPoissonGenericity,
  author = {Álvarez, Nicolás and Becher, Verónica and Cesaratto, Eda and Mereb, Martín and Peres, Yuval and Weiss, Benjamin},
  title = {{Poisson genericity in numeration systems with exponentially mixing probabilities}},
  eprint = {2411.04116},
  eprinttype = {arxiv},
  year = {2026},
  journaltitle = {Transactions of the American Mathematical Society},
  volume = {379},
  number = {5},
  pages = {3403--3423},
  doi = {10.1090/tran/9592}
}

@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{AschenbrennerPong2004,
  author = {Aschenbrenner, Matthias and Pong, Wai-Yan},
  title = {{Orderings of monomial ideals}},
  volume = {181},
  number = {1},
  pages = {27--74},
  year = {2004},
  doi = {10.4064/fm181-1-2},
  journaltitle = {Fundamenta Mathematicae},
  eprint = {math/0305384},
  eprinttype = {arxiv}
}

@article{Barbour1982,
  author = {Barbour, A. D.},
  title = {{{Poisson} convergence and random graphs}},
  volume = {92},
  number = {2},
  pages = {349--359},
  year = {1982},
  doi = {10.1017/S0305004100059995},
  journaltitle = {Mathematical Proceedings of the Cambridge Philosophical Society}
}

@article{BarbourHall1984,
  author = {Barbour, A. D. and Hall, Peter},
  title = {{On the rate of {Poisson} convergence}},
  volume = {95},
  number = {3},
  pages = {473--480},
  year = {1984},
  doi = {10.1017/S0305004100061806},
  journaltitle = {Mathematical Proceedings of the Cambridge Philosophical Society}
}

@article{BasakNathZaharescu2024,
  author = {Basak, Debmalya and Nath, Kunjakanan and Zaharescu, Alexandru},
  title = {{{Poisson} behavior for chains of small quadratic non-residues}},
  volume = {2024},
  number = {4},
  pages = {3356--3390},
  year = {2024},
  doi = {10.1093/imrn/rnad168},
  journaltitle = {International Mathematics Research Notices}
}

@article{CheeKiahPurkayasthaWang2013,
  author = {Chee, Yeow Meng and Kiah, Han Mao and Purkayastha, Punarbasu and Wang, Chengmin},
  title = {{Cross-bifix-free codes within a constant factor of optimality}},
  volume = {59},
  number = {7},
  pages = {4668--4674},
  year = {2013},
  doi = {10.1109/TIT.2013.2252952},
  journaltitle = {IEEE Transactions on Information Theory}
}

@article{ChukovaMinkova2013,
  author = {Chukova, Stefanka and Minkova, Leda D.},
  title = {{Characterization of the {P\'olya--Aeppli} process}},
  volume = {31},
  number = {4},
  pages = {590--599},
  year = {2013},
  doi = {10.1080/07362994.2013.798994},
  journaltitle = {Stochastic Analysis and Applications}
}

@article{Eagleson1977,
  author = {Eagleson, Geoffrey K.},
  title = {{Some simple conditions for limit theorems to be mixing}},
  volume = {21},
  number = {3},
  pages = {637--643},
  year = {1977},
  doi = {10.1137/1121078},
  journaltitle = {Theory of Probability and Its Applications}
}

@article{EisenbudSturmfels1996,
  author = {Eisenbud, David and Sturmfels, Bernd},
  title = {{Binomial ideals}},
  volume = {84},
  number = {1},
  pages = {1--45},
  year = {1996},
  doi = {10.1215/S0012-7094-96-08401-X},
  journaltitle = {Duke Mathematical Journal},
  eprint = {alg-geom/9401001},
  eprinttype = {arxiv}
}

@article{Gouezel2020,
  author = {Gou{\"e}zel, S{\'e}bastien},
  title = {{Variations around {Eagleson's} theorem on mixing limit theorems for dynamical systems}},
  volume = {40},
  number = {12},
  pages = {3368--3374},
  year = {2020},
  doi = {10.1017/etds.2019.42},
  journaltitle = {Ergodic Theory and Dynamical Systems},
  eprint = {1803.11450},
  eprinttype = {arxiv}
}

@online{HarperSoundararajanXu2026,
  author = {Harper, Adam J. and Soundararajan, Kannan and Xu, Max Wenqiang},
  title = {{Distribution of random multiplicative functions in short intervals, with proper normalization}},
  year = {2026},
  eprint = {2606.29040v1},
  eprinttype = {arxiv},
  url = {https://arxiv.org/abs/2606.29040v1}
}

@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{HochmanPaviato2026,
  author = {Hochman, Michael and Paviato, Nicol\`o},
  title = {{A threshold for Poisson behavior of non-stationary product measures}},
  journaltitle = {Ergodic Theory and Dynamical Systems},
  volume = {46},
  number = {4},
  pages = {1009--1019},
  year = {2026},
  doi = {10.1017/etds.2025.10258},
  eprinttype = {arxiv},
  eprint = {2501.11423}
}

@article{Kakutani1948,
  author = {Kakutani, Shizuo},
  title = {{On equivalence of infinite product measures}},
  volume = {49},
  number = {1},
  pages = {214--224},
  year = {1948},
  doi = {10.2307/1969123},
  journaltitle = {Annals of Mathematics}
}

@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}
}

@article{LeCam1960,
  author = {Le Cam, Lucien},
  title = {{An approximation theorem for the {Poisson} binomial distribution}},
  volume = {10},
  number = {4},
  pages = {1181--1197},
  year = {1960},
  doi = {10.2140/pjm.1960.10.1181},
  journaltitle = {Pacific Journal of Mathematics}
}

@article{MatomakiRadziwillTao2016,
  author = {Matom{\"a}ki, Kaisa and Radziwi{\l}{\l}, Maksym and Tao, Terence},
  title = {{Sign patterns of the {Liouville} and {M\"obius} functions}},
  volume = {4},
  year = {2016},
  doi = {10.1017/fms.2016.6},
  journaltitle = {Forum of Mathematics, Sigma},
  eprint = {1509.01545},
  eprinttype = {arxiv},
  eid = {e14}
}

@book{MillerSturmfels2005,
  author = {Miller, Ezra and Sturmfels, Bernd},
  title = {{Combinatorial Commutative Algebra}},
  series = {Graduate Texts in Mathematics},
  volume = {227},
  publisher = {Springer},
  year = {2005},
  doi = {10.1007/b138602},
  location = {New York}
}

@online{NISTDLMF18,
  author = {{NIST Digital Library of Mathematical Functions}},
  title = {{NIST Digital Library of Mathematical Functions: Chapter 18, Orthogonal Polynomials}},
  url = {https://dlmf.nist.gov/18},
  urldate = {2026-09-21},
  version = {1.2.8},
  date = {2026-09-15}
}

@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{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}
}

@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{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}
}

@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{RoquainSchbath2007,
  author = {Roquain, Etienne and Schbath, Sophie},
  title = {{Improved compound {Poisson} approximation for the number of occurrences of any rare word family in a stationary {Markov} chain}},
  volume = {39},
  number = {1},
  pages = {128--140},
  year = {2007},
  doi = {10.1239/aap/1175266472},
  journaltitle = {Advances in Applied Probability}
}

@article{Tao2016TwoPoint,
  author = {Tao, Terence},
  title = {{The logarithmically averaged {Chowla} and {Elliott} conjectures for two-point correlations}},
  volume = {4},
  year = {2016},
  doi = {10.1017/fmp.2016.6},
  journaltitle = {Forum of Mathematics, Pi},
  eprint = {1509.05422},
  eprinttype = {arxiv},
  eid = {e8}
}

@online{Tao2026,
  author = {Tao, Terence},
  title = {{Products of consecutive integers with unusual anatomy}},
  year = {2026},
  eprint = {2603.27990v2},
  eprinttype = {arxiv},
  url = {https://arxiv.org/abs/2603.27990v2}
}

@online{TaoMertens2013,
  author = {Tao, Terence},
  title = {{Mertens' theorems}},
  url = {https://terrytao.wordpress.com/2013/12/11/mertens-theorems/},
  date = {2013-12-11}
}

@article{TaoTeravainen2018,
  author = {Tao, Terence and Ter{\"a}v{\"a}inen, Joni},
  title = {{Odd order cases of the logarithmically averaged {Chowla} conjecture}},
  volume = {30},
  number = {3},
  pages = {997--1015},
  year = {2018},
  doi = {10.5802/jtnb.1062},
  url = {https://www.numdam.org/item/JTNB_2018__30_3_997_0/},
  journaltitle = {Journal de théorie des nombres de Bordeaux}
}

@book{Tenenbaum2015,
  author = {Tenenbaum, G{\'e}rald},
  title = {{Introduction to Analytic and Probabilistic Number Theory}},
  edition = {3},
  series = {Graduate Studies in Mathematics},
  publisher = {American Mathematical Society},
  year = {2015},
  doi = {10.1090/gsm/163},
  location = {Providence, RI},
  number = {163}
}

@article{Turk1980,
  author = {Turk, J.},
  title = {{Multiplicative properties of integers in short intervals}},
  volume = {83},
  number = {4},
  pages = {429--436},
  year = {1980},
  doi = {10.1016/1385-7258(80)90044-X},
  journaltitle = {Indagationes Mathematicae (Proceedings)}
}

@online{Zheng2026,
  author = {Zheng, Guangqu},
  title = {{Four-moment criteria for {Poisson} convergence on {Poisson} and {Rademacher} chaoses}},
  year = {2026},
  eprint = {2608.12451v1},
  eprinttype = {arxiv},
  url = {https://arxiv.org/abs/2608.12451v1}
}

@online{deLaBretecheWangXu2026,
  author = {de la Bret{\`e}che, R{\'e}gis and Wang, Victor Y. and Xu, Max Wenqiang},
  title = {{Random multiplicative functions and making squares from polynomial values}},
  year = {2026},
  eprint = {2607.06398v1},
  eprinttype = {arxiv},
  url = {https://arxiv.org/abs/2607.06398v1}
}