IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2603.21407.html

The Geometry of Heterogeneous Extremes: Optimal Transport and Entropic Design

Author

Listed:
  • I. Sebastian Buhai

Abstract

Extreme economic outcomes are not shaped by tails alone. They are also shaped by unequal access to opportunities. This paper develops a theory of heterogeneous extremes by taking the distribution of opportunity access as the object of study. In a mixed Poisson search setting, normalized maxima admit a Laplace mixture representation that yields order comparisons and a clean benchmark against the homogeneous economy. The main contribution is geometric: a canonical coupling turns differences in heterogeneity into optimal transport bounds for the whole induced law of extremes, the full schedule of top quantiles, and structured counterfactual paths between economies. The paper also derives a second order expansion that separates classical extreme value approximation error from heterogeneity effects. As a complementary normative exercise, it studies an entropy regularized design problem for reallocating opportunities under a mean constraint. A stylized labor market network application interprets heterogeneity as unequal access to job opportunities and shows how the framework can be used for tail counterfactuals and robustness analysis of top wage distributions.

Suggested Citation

  • I. Sebastian Buhai, 2026. "The Geometry of Heterogeneous Extremes: Optimal Transport and Entropic Design," Papers 2603.21407, arXiv.org.
    • Handle: RePEc:arx:papers:2603.21407
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2603.21407
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870, December.
    2. Alfred Galichon, 2016. "Optimal transport methods in economics," Sciences Po Economics Publications (main) hal-03256830, HAL.
    3. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers hal-03256830, HAL.
    4. Zoltán Megyesi, 2002. "Domains of Geometric Partial Attraction of Max-Semistable Laws: Structure, Merge and Almost Sure Limit Theorems," Journal of Theoretical Probability, Springer, vol. 15(4), pages 973-1005, October.
    5. Buhai, I. Sebastian & van der Leij, Marco J., 2023. "A Social Network Analysis of Occupational Segregation," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    6. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Buhai, Ioan-Sebastian, 2026. "The Geometry of Heterogeneous Extremes: Optimal Transport and Entropic Design," IZA Discussion Papers 18511, IZA Network @ LISER.
    2. Jakub Ryłow, 2026. "Topology and Economics: from Sard’s Theorem to Social Choice," Working Papers 2026-9, Faculty of Economic Sciences, University of Warsaw.
    3. Susanne Schennach & Vincent Starck, 2025. "Optimally-Transported Generalized Method of Moments," Papers 2511.05712, arXiv.org.
    4. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Feasible Conditional Belief Distributions," Papers 2307.07672, arXiv.org, revised Nov 2024.
    5. Beatrice Acciaio & Berenice Anne Neumann, 2025. "Characterization of transport optimizers via graphs and applications to Stackelberg–Cournot–Nash equilibria," Mathematics and Financial Economics, Springer, volume 19, number 3, January.
    6. Andrew Lyasoff, 2023. "The Time-Interlaced Self-Consistent Master System of Heterogeneous-Agent Models," Papers 2303.12567, arXiv.org, revised May 2025.
    7. Andrei Voronin, 2025. "Generalized Optimal Transport," Papers 2507.22422, arXiv.org.
    8. João Pedro M. Franco & Márcio Laurini, 2025. "Multivariate Risk Analysis in Cryptocurrency Market: An Optimal Transport Approach," Computational Economics, Springer;Society for Computational Economics, vol. 66(6), pages 5257-5298, December.
    9. Rami V. Tabri, 2026. "Distributional Change in Ordinal Data with Missing Observations: Minimal Mobility and Partial Identification," Papers 2604.12611, arXiv.org, revised Apr 2026.
    10. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers 36/17, Institute for Fiscal Studies.
    11. Kuan‐Ming Chen & Yu‐Wei Hsieh & Ming‐Jen Lin, 2023. "Reducing Recommendation Inequality Via Two‐Sided Matching: A Field Experiment Of Online Dating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1201-1221, August.
    12. Keita Sunada & Kohei Izumi, 2025. "Optimal treatment assignment rules under capacity constraints," Papers 2506.12225, arXiv.org, revised Sep 2025.
    13. Arthur Charpentier & Alfred Galichon & Lucas Vernet, 2019. "Optimal transport on large networks a practitioner guide," Sciences Po Economics Publications (main) hal-02173210, HAL.
    14. S. Viswanathan & Hao Xing, 2026. "Flexible Information Acquisition in the Kyle Model," Papers 2603.21842, arXiv.org.
    15. Jiyuan Tan & Jose Blanchet & Vasilis Syrgkanis, 2026. "Partial Identification of Policy-Relevant Treatment Effects with Instrumental Variables via Optimal Transport," Papers 2604.12263, arXiv.org, revised Apr 2026.
    16. Wesley Phoa, 2026. "A Double Categorical Framework for Multi-Stage Portfolio Construction and Alignment," Papers 2603.12301, arXiv.org.
    17. Xinran Liu, 2026. "Recovering Counterfactual Distributions via Wasserstein GANs," Papers 2601.17296, arXiv.org.
    18. Yagan Hazard & Toru Kitagawa, 2025. "Who With Whom? Learning Optimal Matching Policies," Papers 2507.13567, arXiv.org.
    19. Alfred Galichon & Marc Henry, 2026. "An econometrician's guide to optimal transport," Papers 2604.04227, arXiv.org.
    20. Cetin, Umut, 2025. "Insider trading with penalties in continuous time," LSE Research Online Documents on Economics 128957, London School of Economics and Political Science, LSE Library.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2603.21407. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.