[2407.02415] The Symplectic Schur Process Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematical Physics arXiv:2407.02415 (math-ph) [Submitted on 2 Jul 2024 ( v1 ), last revised 29 Apr 2026 (this version, v3)] Title: The Symplectic Schur Process Authors: Cesar Cuenca , Matteo Mucciconi View a PDF of the paper titled The Symplectic Schur Process, by Cesar Cuenca and Matteo Mucciconi View PDF HTML (experimental) Abstract: We define a measure on tuples of partitions, called the symplectic Schur process, that should be regarded as the right analogue of the Schur process of Okounkov-Reshetikhin for the Cartan type C. The weights of our measure include factors that are universal symplectic characters, as well as a novel family of "Down-Up Schur functions" that we define and for which we prove new identities of Cauchy-Littlewood-type. Our main structural result is that the point process corresponding to the symplectic Schur process is determinantal and we find an explicit correlation kernel. We also present dynamics that preserve the family of symplectic Schur processes and explore an alternative sampling scheme, based on the Berele insertion algorithm, in a special case. Finally, we study the asymptotics of the Berele insertion process and find explicit formulas for the limit shape and fluctuations near the bulk and the edge. One of the limit regimes leads to a new kernel that resembles the symmetric Pearcey kernel. Comments: v2: Added interpretation of Berele insertion algorithm in terms of half-triangular interlacing arrays in the intro. Fixed typos and added references. v3: Several minor editorial changes; added two references. 58 pages, 8 figures Subjects: Mathematical Physics (math-ph) ; Combinatorics (math.CO); Probability (math.PR) MSC classes: 05E05, 60K35, 82B23, 05A19 Cite as: arXiv:2407.02415 [math-ph] (or arXiv:2407.02415v3 [math-ph] for this version) https://doi.org/10.48550/arXiv.2407.02415 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Cesar Cuenca [ view email ] [v1] Tue, 2 Jul 2024 16:41:53 UTC (6,459 KB) [v2] Sat, 1 Mar 2025 22:20:29 UTC (6,711 KB) [v3] Wed, 29 Apr 2026 07:48:57 UTC (3,767 KB) Full-text links: Access Paper: View a PDF of the paper titled The Symplectic Schur Process, by Cesar Cuenca and Matteo Mucciconi View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2024-07 Change to browse by: math math.CO math.MP math.PR References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from