{"id":170,"date":"2023-06-15T15:35:08","date_gmt":"2023-06-15T22:35:08","guid":{"rendered":"https:\/\/live-usc-dornsife.pantheonsite.io\/nicolai-haydn\/?page_id=170"},"modified":"2025-10-16T13:39:24","modified_gmt":"2025-10-16T20:39:24","slug":"research-papers","status":"publish","type":"page","link":"https:\/\/dornsife.usc.edu\/nicolai-haydn\/research-papers\/","title":{"rendered":"Research papers"},"content":{"rendered":"\n\n  \n    \n\n\n\n\n\n\n<div\n  class=\"cc--component-container cc--rich-text \"\n\n  \n  \n  \n  \n  \n  \n  >\n  <div class=\"c--component c--rich-text\"\n    \n      >\n\n    \n      \n<div class=\"f--field f--wysiwyg\">\n\n    \n  <ul>\n<li>N Haydn and G Park: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2025\/10\/Convolution2.pdf\">Higher Order Return Times for \\phi-Mixing Measures<\/a>; USC preprint<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2025\/10\/Sacker24.pdf\">Return times distribution of expanding maps<\/a>; USC preprint<\/li>\n<li>L Amorim, N Haydn and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2025\/02\/RandomNull22.pdf\">Quenched limiting entry distributions for random expanding maps with null targets<\/a>; Stochastic Processes and their Applications, 179 (2025), p. 104511<\/li>\n<li>S Gallo, N Haydn and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/NSS2021-07.pdf\">Number of Visits in Arbitrary Sets for $\\phi$-mixing Dynamics<\/a>; Ann. Inst. H. Poincare Probab. Statist. 60(2), 1150\u20131187 (2024)<\/li>\n<li>N Haydn and M Nicol: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/ErdosRenyi210201.pdf\">Erd\u00f6s-Renyi laws for exponentially and polynomially mixing dynamical systems<\/a><\/li>\n<li>C Davis, N Haydn and F Yang: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/EscapeNullSet08.pdf\">Escape rate and conditional escape rate from a probabilistic point of view<\/a>; Annales Henri Poincare, 22, 2195\u20132225 (2021)<\/li>\n<li>J Atnip, N Haydn and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/EVT_proceed_baker_6.pdf\">Extreme Value Theory with Spectral Techniques: Application to a Simple Attractor<\/a><\/li>\n<li>N Haydn and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/PeriodicGeometric6.pdf\">Limiting Entry Times Distribution for Arbitrary Null Sets<\/a>; Comm. Math. Phys. 378(4), (2020)<\/li>\n<li>N Haydn and F Yang: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/LocalEscape8.pdf\">Local Escape Rates for \u03c6-mixing Dynamical Systems<\/a>; Ergod. Th. &amp; Dynam. Sys. Vol. 40 (10), p.2854\u20132880 (2020).<\/li>\n<li>N Haydn, J Rousseau and F Yang: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/RandomMaps11.pdf\">Exponential Law for Random Maps on Compact Manifolds<\/a>; Nonlinearity, 33(12), 6760\u20136789 (2020)<\/li>\n<li>N Haydn and F Yang: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/GeoPoisson5.pdf\">A Derivation of the Poisson Law for Returns of Smooth Maps with Certain Geometrical Properties<\/a>; in Contemporary Mathematics Proceedings in memoriam Chernov 2017<\/li>\n<li>N Haydn and M Todd: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/RanPoisson_rev2.pdf\">Return times at periodic points in random dynamics<\/a>; Nonlinearity <strong>30(1) <\/strong>(2017), 73\u201389<\/li>\n<li>N Haydn, M Nicol, A T\u00f6r\u00f6k and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/asip_seq_sv15.pdf\">Almost sure invariance principle for sequential and non-stationary dynamical systems<\/a>; Transactions of the AMS, 369(8), 5293\u20135316, (2017)<\/li>\n<li>N Haydn and F Yang: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Bowenballs6.pdf\">Entry times distribution for dynamical balls on metric spaces<\/a>; J. Stat. Phys. (2017) DOI: 10.1007\/s10955-017-1745-7.<\/li>\n<li>N Haydn and F Yang: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/HaydnYang16.pdf\">Entry times distribution for mixing systems<\/a>; J. Stat. Phys. (2016) DOI 10.1007\/s10955-016-1487-y.<\/li>\n<li>N Haydn and K Wasilewska: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/HaWa15.pdf\">Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamics systems<\/a>; Disc. Cont. Dynam. Syst. <strong>36(5)<\/strong> (2106), 2585\u20132611.<\/li>\n<li>J M Freitas, N Haydn and M Nicol: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/FreitasHN14.pdf\">Convergence of Rare Events Point Processes to the Poisson Process for Planar Billiards<\/a>; Nonlinearity <strong>27(7)<\/strong> (2014), 1669\u20131687.<\/li>\n<li>N Haydn and M Kupsa: Example of a non-standard Extremal Values Law; Ergod. Th. &amp; Dynam. Syst. <strong>35(6)<\/strong> (2015), 1902\u20131912.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/dsaij_special_haydn.pdf\">Entry and Return Times Distribution<\/a>; Dynamical Systems <strong>28(3)<\/strong> (2013), 333\u2013353.<\/li>\n<li>N Haydn, N Winterberg and R Zweim\u00fcller: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Returning_Hitting_and_Inducing_REV_10.pdf\">Return-times statistics, Hitting-time statistic and Inducing<\/a>; BIRS Proceedings 2014.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/ASIPbeta.pdf\">The Almost Sure Invariance Principle for Beta-Mixing measures<\/a>; J. Stat. Phys. <strong>159(2)<\/strong> (2015), 231\u2013254.<\/li>\n<li>C Gupta, N Haydn, M Ko and A Rada: <a href=\"\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/09\/GHKR15.pdf\">Entrance Time Convergence and Entropy<\/a>; Stoch. Dynam. <strong>15(4)<\/strong> (2015).<\/li>\n<li>N Haydn, M Nicol, S Vaienti and L Zhang: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/HayNVZ13.pdf\">Central Limit Theorems for the shrinking target problem<\/a>; J. Stat Phys. <strong>153<\/strong> (2013), 864\u2013887.<\/li>\n<li>C Gupta and N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/CML4.pdf\">Statistical properties of coupled expanding maps on a lattice with general infinite range couplings and H\u00f6lder densities<\/a><\/li>\n<li>N Haydn, M Nicol, T Persson and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Borel_mix_final.pdf\">A note on the Borel-Cantelli lemmas for non-uniformly hyperbolic dynamical systems<\/a>; Erg. Th. &amp; Dynam. Syst.<strong>33(2)<\/strong> (2013), 475\u2013498.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/PhasetransitionsDCDS.pdf\">Phase transitions in one-dimensional subshifts<\/a>: Disc. Cont. Dynam. Syst. <strong>33(5)<\/strong> (2013), 1965\u20131973.<\/li>\n<li>G Cristadoro, N Haydn, P Marie and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Pilo_final.g3.pdf\">Statistical properties of intermittened maps with unbounded derivative<\/a>; Nonlinearity 23 (2010), 1071\u20131095.<\/li>\n<li>N Haydn and Y Psiloyenis: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/HayPsil14.pdf\">Return times distribution for Markov towers with decay of correlations<\/a>; Nonlinearity <strong>27(6)<\/strong> (2014), 1323\u20131349.<\/li>\n<li>N Haydn and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/RenyiEntropyETDS.pdf\">The R\u00e9nyi Entropy and the Large Deviation of Short Return Times<\/a>; Ergod. Th. &amp; Dynam. Syst. <strong>30<\/strong> (2010), 159\u2013179.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Haydn12.pdf\">The Central Limit Theorem for uniformly mixing systems<\/a>; Stochastics and Dynamics <strong>12(4)<\/strong> (2012).<\/li>\n<li>N Haydn, E Lunedei and S Vaienti: <a href=\"\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/09\/Lunedei5.pdf\">Averaged number of visits<\/a>; Chaos <strong>17<\/strong> (2007).<\/li>\n<li>N Haydn and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/HayVai09.pdf\">The compound Poisson distribution and return times in dynamical systems<\/a>; Prob. Th. &amp; Rel. Fields <strong>144<\/strong> (2009), 517\u2013542.<\/li>\n<li>N Haydn, E Lunedei, L Rossi, G Turchetti and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/BolognaPR.pdf\">Multiple returns for some regular and mixing maps<\/a>; Chaos <strong>15(3)<\/strong> (2005).<\/li>\n<li>P Ferraro, N Haydn and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Fluctuations5.pdf\">Entropy fluctuations for parabolic maps<\/a>; Nonlinearity <strong>16<\/strong> (2003), 1203\u20131218.<\/li>\n<li>N Haydn, Y Lacroix and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/NSY.pdf\">Hitting and return times in ergodic dynamical systems<\/a>; Ann. Prob. <strong>33<\/strong> (2005), 2043\u20132050.<\/li>\n<li>N Haydn: The distribution of the measure of cylinder sets for non-Gibbsian measures;in <em>Complex Dynamics and Related Topics<\/em> 2004, 147\u2013162.<\/li>\n<li>E Gutkin and N Haydn: Generalised polygon exchanges with zero topological entropy; Proceedings of Workshop on Dynamical Systems, University of Maryland 1993, 12\u201318.<\/li>\n<li>N Haydn and S Vaienti: The Central Limit Theorem for (\\phi,f)-mixing systems; Stoch. &amp; Dynamics <strong>4<\/strong> (2004), 595\u2013627.<\/li>\n<li>N Haydn and S Vaienti: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Haydn787.pdf\">The limiting distribution and error terms for return times of dynamial systems<\/a>; Disc. Cont. Dynam. Syst. <strong>10(3)<\/strong> (2004), 589\u2013616.<\/li>\n<li>N Haydn: <a href=\"\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/09\/Interval4.pdf\">Convergence of the natural approximatipns of monotone interval maps<\/a>; Chaos 2004.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Expanding.maps2_.pdf\">Generalised Gibbs states for expanding maps<\/a><\/li>\n<li>N Haydn, Luevano, G Mantica and S Vaienti: Multifractal Properties of Return Time Statistics; Phys. Rev. Letters <strong>88<\/strong> (2002).<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Distribution2.pdf\">The Distribution of the First Return time for Rational Maps<\/a>; J. Stat. Phys. <strong>94<\/strong> (1999), 1027\u20131036.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Poisson4.pdf\">Statistical Properties of Equilibrium States for Rational Maps<\/a>; Ergod. Th. &amp; Dynam. Syst. <strong>20<\/strong> (2000), 1371\u20131390.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Convergence.pdf\">Convergence of the Transfer Operator for Rational Maps<\/a>; Ergod. Th. &amp; Dynam. Syst. <strong>19<\/strong> (1999), 657\u2013669.<\/li>\n<li>N Haydn and S Isola: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/pjulia5.pdf\">Parabolic rational maps<\/a>; Journal LMS <strong>63<\/strong> (2001), 673&#8211;689.<\/li>\n<li>E Gutkin and N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Subexponential.pdf\">Entropy of some generalised polygon exchange maps and polygonal billiards<\/a>; Ergod. Th. &amp; Dynam. Syst. <strong>17<\/strong> (1997).<\/li>\n<li>E Gutkin and N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/polygabs.pdf\">The Topological Entropy of Generalised Polygon Exchanges<\/a>; Bull. AMS <strong>32<\/strong> (1995), 50\u201356.<\/li>\n<li>N Haydn: Classification of Gibbs&#8217; states on Smale spaces and one-dimensional lattice systems; Nonlinearity <strong>7<\/strong> (1994), 345\u2013366.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/CanonicalProduct94.pdf\">Canonical product structure of equilibrium states<\/a>; Random &amp; Computational Dynamics <strong>2<\/strong> (1994), 79\u201396.<\/li>\n<li>N Haydn: Gibbs measures for Axiom A flows; J Stat. Phys. <strong>72<\/strong> (1993), 309\u2013327.<\/li>\n<li>N Haydn and D Ruelle: Equivalence of Gibbs and Equilibrium States for Homeomorphism Satisfying Expansiveness and Specification; Commun. Math. Phys <strong>148<\/strong> (1992), 155\u2013167.<\/li>\n<li>N Haydn: The product structure on finitely presented systems; Israel J. Math. <strong>73<\/strong> (1991), 343\u2013356.<\/li>\n<li>N Haydn: <a href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/wp-content\/uploads\/sites\/220\/2023\/06\/Haydn90.pdf\">Gibbs Functionals of Subshifts<\/a>; Commun. Math. Phys. <strong>134<\/strong> (1990), 217\u2013236.<\/li>\n<li>N Haydn: Meromorphic extension of the zeta function for Axiom A flows; Ergod. Th. &amp; Dynam. Syst. <strong>10<\/strong> (1990), 347\u2013360.<\/li>\n<li>N Haydn: On invariant curves under renormalisation; Nonlinearity <strong>3<\/strong> (1990), 887\u2013912.<\/li>\n<li>N Haydn: On Gibbs and Equilibrium states; Ergod. Th &amp; Dynam. Syst. <strong>7<\/strong> (1987), 119\u2013132.<\/li>\n<\/ul>\n\n\n\n<\/div>\n\n\n  <\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":370,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-170","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Research papers - Nicolai Haydn<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/research-papers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research papers - Nicolai Haydn\" \/>\n<meta property=\"og:url\" content=\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/research-papers\/\" \/>\n<meta property=\"og:site_name\" content=\"Nicolai Haydn\" \/>\n<meta property=\"article:modified_time\" content=\"2025-10-16T20:39:24+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/research-papers\/\",\"url\":\"https:\/\/dornsife.usc.edu\/nicolai-haydn\/research-papers\/\",\"name\":\"Research papers - 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