Fernando Cordero

My research lies at the interface of stochastic processes and population genetics. A central theme of my work is the establishment of dualities that connect the forward-in-time evolution of a population with its underlying ancestral processes. These dualities form a rigorous bridge between future and past evolution, translating questions about type frequencies into statements about lineages, and vice versa. A particular challenge of my research is to uncover the intuition behind these relations, so that they emerge naturally from individual-based mechanisms rather than appearing as identities arising from a black box. All of this is embedded in a probabilistic framework in which evolutionary change is driven by chance.

News

February 2026: We warmly welcome Hanna Franke to our institute as a new PhD student. Hanna joins us from Berlin, where she completed her Master of Science in Physics at Humboldt University of Berlin. In her Master’s thesis, titled “Underdamped Brownian Motion under Poissonian Reset”, she investigated stochastic dynamics beyond the overdamped regime, focusing on reset processes in nonequilibrium systems. We are very pleased to have her join our group and look forward to her contributions to our research.
February 2026: We are pleased to welcome Zsófia Talyigás to our institute as a postdoctoral researcher. Prior to joining us, she was a member of the Biomathematics group of Emmanuel Schertzer at the University of Vienna. Her research lies in probability theory, with a focus on branching processes with selection—models describing the evolution of populations under natural selection. We are very happy to have her with us and look forward to her contributions.

Preprints

E. Baake, F. Cordero, E. Di Gaspero, A. Wakolbinger. Killing versus catastrophes in birth-death processes and an application to population genetics.

[arXiv]

@misc{baake2024killingcatastrophes,
  author        = {Baake, Ellen and Cordero, Fernando and Di Gaspero, E. and Wakolbinger, Anton},
  title         = {Killing versus catastrophes in birth-death processes and an application to population genetics},
  year          = {2024},
  eprint        = {2407.08478},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2407.08478}
}

E. Baake, F. Cordero, S.M. Mellis, V. Wachtel. Critical multitype branching: a functional limit theorem and ancestral processes.

[arXiv]

@misc{baake2025criticalmultitype,
  author        = {Baake, E- and Cordero, F. and Mellis, S. M. and Wachtel, V.},
  title         = {Critical multitype branching: a functional limit theorem and ancestral processes},
  year          = {2025},
  eprint        = {2504.21714},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2504.21714}
}

F. Cordero, G. Véchambre. Distance to stationarity and open set recurrence for ergodic processes on the unit interval with a Bernstein or a Siegmund dual.

[arXiv]

@misc{cordero2025distancestationarity,
  author        = {Cordero, Fernando and V{\'e}chambre, Gr{\'e}goire},
  title         = {Distance to stationarity and open set recurrence for ergodic processes on the unit interval with a Bernstein or a Siegmund dual},
  year          = {2025},
  eprint        = {2507.07587},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2507.07587}
}

F. Cordero, A. González Casanova, J. Schweinsberg. Two waves of adaptation: speciation induced by dormancy in a model with changing environment.

[arXiv]

@misc{cordero2024twowavesadaptation,
  author        = {Cordero, F. and Gonz{\'a}lez Casanova, A. and Schweinsberg, J.},
  title         = {Two waves of adaptation: speciation induced by dormancy in a model with changing environment},
  year          = {2024},
  eprint        = {2410.10890},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2410.10890}
}

F. Cordero, S.M. Mellis, E. Schertzer. Structured coalescents, coagulation equations and multi-type branching processes.

[arXiv]

@misc{cordero2025structuredcoalescents,
  author        = {Cordero, F. and Mellis, S. M. and Schertzer, E.},
  title         = {Structured coalescents, coagulation equations and multi-type branching processes},
  year          = {2025},
  eprint        = {2505.09400},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2505.09400}
}

F. Alberti, F. Boenkost, F. Cordero. On the block size spectrum of a class of exchangeable dynamic random graphs.

[arXiv]

@misc{alberti2024blocksizespectrum,
  author        = {Alberti, F. and Boenkost, F. and Cordero, F.},
  title         = {On the block size spectrum of a class of exchangeable dynamic random graphs},
  year          = {2024},
  eprint        = {2406.08972},
  archivePrefix = {arXiv},
  url           = {https://arxiv.org/abs/2406.08972}
}

Publications

2026 — F. Cordero, C. Jorquera, H. Olivero, L. Videla. Wright–Fisher kernels: from linear to non-linear dynamics, ergodicity and McKean–Vlasov scaling limits. Electron. J. Probab., In press. EJP

[arXiv]

@misc{cordero2024wrightfisherkernels,
  author        = {Cordero, Fernando and Jorquera, C. and Olivero, H. and Videla, L.},
  title         = {Wright--Fisher kernels: from linear to non-linear dynamics, ergodicity and McKean--Vlasov scaling limits},
    journal = {Electron. J. Probab., In Press.},
  year    = {2026},
  url           = {}
}

2026 — G. Alsmeyer, F. Cordero, H. Dopmeyer. A two-size Wright–Fisher Model: asymptotic Analysis via Uniform Renewal Theory. Stochastic Process. Appl., 192, 104812. SPA

[Journal] [arXiv]

@article{alsmeyer_cordero_dopmeyer_2026_twosize_wf,
  author  = {Alsmeyer, G. and Cordero, F. and Dopmeyer, H.},
  title   = {A two-size Wright--Fisher Model: asymptotic Analysis via Uniform Renewal Theory},
  journal = {Stochastic Process. Appl.},
  year    = {2026},
  volume  = {192},
  pages   = {104812},
  doi     = {10.1016/j.spa.2025.104812},
  url     = {https://doi.org/10.1016/j.spa.2025.104812}
}

2026 — F. Cordero, S. Hummel, G. Véchambre. Bernstein duality revisited: frequency-dependent selection, coordinated mutation and opposing environments. Bernoulli, 32(2), 874–900. Bernoulli

[Journal] [arXiv]

@article{cordero_hummel_vechambre_2026_bernstein_duality_revisited,
  author  = {Cordero, Fernando and Hummel, Sebastian and V{\'e}chambre, Gr{\'e}goire},
  title   = {Bernstein duality revisited: frequency-dependent selection, coordinated mutation and opposing environments},
  journal = {Bernoulli},
  year    = {2026},
  volume  = {32},
  number  = {2},
  pages   = {874--900},
  doi     = {10.3150/25-BEJ1883},
  url     = {https://doi.org/10.3150/25-BEJ1883}
}

2025 — F. Cordero, S. Hummel, G. Véchambre. Λ-Wright–Fisher processes with general selection and opposing environmental effects: fixation and coexistence. Ann. Appl. Probab., 35(1), 393–457. AAP

[Journal] [arXiv]

@article{cordero_hummel_vechambre_2025_lambda_wf_selection_environments,
  author  = {Cordero, Fernando and Hummel, Sebastian and V{\'e}chambre, Gr{\'e}goire},
  title   = {{$\Lambda$}-Wright--Fisher processes with general selection and opposing environmental effects: fixation and coexistence},
  journal = {The Annals of Applied Probability},
  year    = {2025},
  volume  = {35},
  number  = {1},
  pages   = {393--457},
  doi     = {10.1214/24-AAP2117},
  url     = {https://doi.org/10.1214/24-AAP2117}
}

2024 — E. Baake, F. Cordero, E. Di Gaspero. The mutation process on the ancestral line under selection. Theor. Popul. Biol., 158, 60–75. TPB

[Journal] [arXiv]

@article{baake_cordero_digaspero_2024_mutation_ancestral_line_selection,
  author  = {Baake, E. and Cordero, Fernando and Di Gaspero, E.},
  title   = {The mutation process on the ancestral line under selection},
  journal = {Theoretical Population Biology},
  year    = {2024},
  volume  = {158},
  pages   = {60--75},
  doi     = {10.1016/j.tpb.2024.04.004},
  url     = {https://doi.org/10.1016/j.tpb.2024.04.004}
}

2023 — F. Cordero, G. Véchambre. Moran models and Wright–Fisher diffusions with selection and mutation in a one-sided random environment. Adv. in Appl. Probab., 55, 701–767. APT

[Journal] [arXiv]

@article{cordero_vechambre_2023_moran_wf_random_environment,
  author  = {Cordero, Fernando and V{\'e}chambre, Gr{\'e}goire},
  title   = {Moran models and Wright--Fisher diffusions with selection and mutation in a one-sided random environment},
  journal = {Advances in Applied Probability},
  year    = {2023},
  volume  = {55},
  pages   = {701--767},
  doi     = {10.1017/apr.2022.54},
  url     = {https://doi.org/10.1017/apr.2022.54}
}

2022 — E. Baake, F. Cordero, S. Hummel. Lines of descent in the deterministic mutation-selection model with pairwise interaction. Ann. Appl. Probab., 32, 2400–2447. AAP

[Journal] [arXiv]

@article{baake_cordero_hummel_2022_lines_of_descent_pairwise_interaction,
  author  = {Baake, E. and Cordero, F. and Hummel, S.},
  title   = {Lines of descent in the deterministic mutation-selection model with pairwise interaction},
  journal = {The Annals of Applied Probability},
  year    = {2022},
  volume  = {32},
  pages   = {2400--2447},
  doi     = {10.1214/21-AAP1736},
  url     = {http://dx.doi.org/10.1214/21-AAP1736}
}

2022 — F. Cordero, S. Hummel, E. Schertzer. General selection models: Bernstein duality and minimal ancestral structures. Ann. Appl. Probab., 32, 1499–1556. AAP

[Journal] [arXiv]

@article{cordero_hummel_schertzer_2022_general_selection_models,
  author  = {Cordero, Fernando and Hummel, S. and Schertzer, E.},
  title   = {General selection models: Bernstein duality and minimal ancestral structures},
  journal = {The Annals of Applied Probability},
  year    = {2022},
  volume  = {32},
  pages   = {1499--1556},
  doi     = {10.1214/21-AAP1683},
  url     = {https://doi.org/10.1214/21-AAP1683}
}

2022 — F. Cordero, A. González Casanova, J. Schweinsberg, M. Wilke-Berenguer. Λ-coalescents arising in populations with dormancy. Electron. J. Probab., 27, 1–34. EJP

[Journal] [arXiv]

@article{cordero_gonzalezcasanova_schweinsberg_wilkeberenguer_2022_lambda_coalescents_dormancy,
  author  = {Cordero, Fernando and Gonz{\'a}lez Casanova, A. and Schweinsberg, J. and Wilke-Berenguer, M.},
  title   = {{$\Lambda$}-coalescents arising in populations with dormancy},
  journal = {Electronic Journal of Probability},
  year    = {2022},
  volume  = {27},
  pages   = {1--34},
  doi     = {10.1214/22-EJP739},
  url     = {https://doi.org/10.1214/22-EJP739}
}

2019 — F. Cordero, M. Möhle. On the stationary distribution of the block counting process for population models with mutation and selection. J. Math. Anal. Appl., 474, 1049–1081. JMAA

[Journal] [arXiv]

@article{cordero_mohle_2019_stationary_distribution_block_counting,
  author  = {Cordero, Fernando and M{\"o}hle, M.},
  title   = {On the stationary distribution of the block counting process for population models with mutation and selection},
  journal = {Journal of Mathematical Analysis and Applications},
  year    = {2019},
  volume  = {474},
  pages   = {1049--1081},
  doi     = {10.1016/j.jmaa.2019.02.004},
  url     = {https://doi.org/10.1016/j.jmaa.2019.02.004}
}

2018 — F. Cordero, I. Klein, L. Perez-Ostafe. Asymptotic arbitrage in fractional mixed markets. Mod. Stoch. Theory Appl., 5, 415–428. MSTA

[Journal] [arXiv]

@article{cordero_klein_perezostafe_2018_asymptotic_arbitrage_fractional_mixed,
  author  = {Cordero, Fernando and Klein, I. and Perez-Ostafe, L.},
  title   = {Asymptotic arbitrage in fractional mixed markets},
  journal = {Modern Stochastic Theory and Applications},
  year    = {2018},
  volume  = {5},
  pages   = {415--428},
  doi     = {10.15559/18-VMSTA109},
  url     = {https://doi.org/10.15559/18-VMSTA109}
}

2018 — E. Baake, F. Cordero, S. Hummel. A probabilistic view on the deterministic mutation-selection equation: dynamics, equilibria, and ancestry via individual lines of descent. J. Math. Biol., 77, 795–820. JMB

[Journal] [arXiv]

@article{baake_cordero_hummel_2018_probabilistic_view_mutation_selection,
  author  = {Baake, E. and Cordero, Fernando and Hummel, S.},
  title   = {A probabilistic view on the deterministic mutation-selection equation: dynamics, equilibria, and ancestry via individual lines of descent},
  journal = {Journal of Mathematical Biology},
  year    = {2018},
  volume  = {77},
  pages   = {795--820},
  url     = {https://link.springer.com/article/10.1007/s00285-018-1228-8}
}

2017 — F. Cordero. The deterministic limit of the Moran model: a uniform central limit theorem. Markov Process. Related Fields, 23, 313–324. MPRF

[Journal] [arXiv]

@article{cordero2017_deterministic_limit_moran_uniform_clt,
  author  = {Cordero, Fernando},
  title   = {The deterministic limit of the Moran model: a uniform central limit theorem},
  journal = {Markov Processes and Related Fields},
  year    = {2017},
  volume  = {23},
  pages   = {313--324},
  url     = {http://math-mprf.org/journal/articles/id1466/}
}

2017 — F. Cordero. Common ancestor type distribution: a Moran model and its deterministic limit. Stochastic Process. Appl., 127, 590–621. SPA

[Journal] [arXiv]

@article{cordero2017_common_ancestor_type_distribution,
  author  = {Cordero, Fernando},
  title   = {Common ancestor type distribution: a Moran model and its deterministic limit},
  journal = {Stochastic Processes and Applications},
  year    = {2017},
  volume  = {127},
  pages   = {590--621},
  doi     = {10.1016/j.spa.2016.06.019},
  url     = {https://doi.org/10.1016/j.spa.2016.06.019}
}

2016 — F. Cordero, L. Perez-Ostafe. Strong asymptotic arbitrage in the large fractional binary market. Math. Financ. Econ., 10, 179–202. MFE

[Journal] [arXiv]

@article{cordero_perezostafe_2016_strong_asymptotic_arbitrage_large_fractional_binary,
  author  = {Cordero, Fernando and Perez-Ostafe, L.},
  title   = {Strong asymptotic arbitrage in the large fractional binary market},
  journal = {Mathematical Finance and Economics},
  year    = {2016},
  volume  = {10},
  pages   = {179--202},
  url     = {https://link.springer.com/article/10.1007/s11579-015-0155-3}
}

2016 — F. Cordero, I. Klein, L. Perez-Ostafe. Asymptotic proportion of arbitrage points in fractional binary markets. Stochastic Process. Appl., 126, 315–336. SPA

[Journal] [arXiv]

@article{cordero_klein_perezostafe_2016_asymptotic_proportion_arbitrage_points,
  author  = {Cordero, Fernando and Klein, I. and Perez-Ostafe, L.},
  title   = {Asymptotic proportion of arbitrage points in fractional binary markets},
  journal = {Stochastic Processes and Applications},
  year    = {2016},
  volume  = {126},
  pages   = {315--336},
  doi     = {10.1016/j.spa.2015.09.002},
  url     = {https://doi.org/10.1016/j.spa.2015.09.002}
}

2016 — F. Cordero. The first passage time of a stable process conditioned to not overshoot. J. Theor. Probab., 29, 776–796. JTP

[Journal] [arXiv]

@article{cordero2016_first_passage_stable_process_conditioned_not_overshoot,
  author  = {Cordero, Fernando},
  title   = {The first passage time of a stable process conditioned to not overshoot},
  journal = {Journal of Theoretical Probability},
  year    = {2016},
  volume  = {29},
  pages   = {776--796},
  url     = {https://link.springer.com/article/10.1007/s10959-014-0592-6}
}

2015 — F. Cordero, L. Perez-Ostafe. Critical transaction costs and 1-step asymptotic arbitrage in fractional binary markets. Int. J. Theor. Appl. Finan., 18. IJTAF

[Journal] [arXiv]

@article{cordero_perezostafe_2015_critical_transaction_costs_onestep_arbitrage,
  author  = {Cordero, Fernando and Perez-Ostafe, L.},
  title   = {Critical transaction costs and 1-step asymptotic arbitrage in fractional binary markets},
  journal = {International Journal of Theoretical and Applied Finance},
  year    = {2015},
  volume  = {18},
  doi     = {10.1142/S0219024915500296},
  url     = {https://doi.org/10.1142/S0219024915500296}
}

2014 — F. Cordero, I. Klein, L. Perez-Ostafe. Binary markets under transaction costs. Int. J. Theor. Appl. Finan., 17. IJTAF

[Journal] [arXiv]

@article{cordero_klein_perezostafe_2014_binary_markets_transaction_costs,
  author  = {Cordero, Fernando and Klein, I. and Perez-Ostafe, L.},
  title   = {Binary markets under transaction costs},
  journal = {International Journal of Theoretical and Applied Finance},
  year    = {2014},
  volume  = {17},
  doi     = {10.1142/S0219024914500307},
  url     = {https://doi.org/10.1142/S0219024914500307}
}

2011 — F. Cordero. On the scaling property in fluctuation theory for stable Lévy processes. SIAM Theory Probab. Appl., 55, 683–691. SIAM

[Journal] [arXiv]

@article{cordero2011_scaling_property_fluctuation_stable_levy,
  author  = {Cordero, Fernando},
  title   = {On the scaling property in fluctuation theory for stable L{\'e}vy processes},
  journal = {SIAM Theory of Probability and Applications},
  year    = {2011},
  volume  = {55},
  pages   = {683--691},
  doi     = {10.1137/S0040585X97985157},
  url     = {https://doi.org/10.1137/S0040585X97985157}
}

Contact

Address: Gregor Mendel Straße 33, 1180 Vienna

Email:

Fernando Cordero

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