https://m2.mtmt.hu/ eng 2026-05-26 10:40 PublicationOther 35447049 ADMIN_APPROVED true 0 false 2025-05-13T10:42:41.475+0000 2024-12-03T13:46:59.327+0000 2024-10-10T11:06:20.779+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 2025-04-02T14:18:36.149+0000 2025-04-02T14:18:36.149+0000 2024-12-03T13:46:59.331+0000 true 10003134 Wolf György /api/admin/10003134 Admin true 10003134 Admin 10080081 /api/admin/10080081 Bavalicsné Kerekes Beáta true true Admin 10067876 /api/admin/10067876 Ladányi Gusztáv true true 2024-10-30T14:44:14.592+0000 true true 29 29 /api/publicationtype/29 PublicationType 15 true 29 PublicationOther true 10000361 Publication in repository true 29 29 /api/publicationtype/29 PublicationType 15 true 29 PublicationOther /api/subtype/10000361 Csak repozitóriumban hozzáférhető közlemény SubType 1582 true 10000361 true 1 /api/category/1 Category true 1 Pablo, Candela On Fω2-affine-exchangeable probability measures 2203.08915 2203.08915 62 2024 For any standard Borel space B, let P(B) denote the space of Borel probability measures on B. In relation to a difficult problem of Aldous in exchangeability theory, and in connection with arithmetic combinatorics, Austin raised the question of describing the structure of affine-exchangeable probability measures on product spaces indexed by the vector space Fω2, i.e., the measures in P(BFω2) that are invariant under the coordinate permutations on BFω2 induced by all affine automorphisms of Fω2. We answer this question by describing the extreme points of the space of such affine-exchangeable measures. We prove that there is a single structure underlying every such measure, namely, a random infinite-dimensional cube (sampled using Haar measure adapted to a specific filtration) on a group that is a countable power of the 2-adic integers. Indeed, every extreme affine-exchangeable measure in P(BFω2) is obtained from a P(B)-valued function on this group, by a vertex-wise composition with this random cube. The consequences of this result include a description of the convex set of affine-exchangeable measures in P(BFω2) equipped with the vague topology (when B is a compact metric space), showing that this convex set is a Bauer simplex. We also obtain a correspondence between affine-exchangeability and limits of convergent sequences of (compact-metric-space valued) functions on vector spaces Fn2 as n→∞. Via this correspondence, we establish the above-mentioned group as a general limit domain valid for any such sequence. 2024 true false false false GREEN 2025-05-13 true http://real.mtak.hu/207266 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 false false false false 2024-11-13T08:46:44.295+0000 Mesterséges Intelligencia (HRN RAMKI) 2 8 1 3 0 false 10080081 10067876 Language 10002 /api/language/10002 Angol English true 2 true PersonAuthorship 120835661 /api/authorship/120835661 1 0.33333334 true false Pablo Candela true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 120835662 /api/authorship/120835662 2 0.33333334 false false Author 10076661 /api/author/10076661 Gonzalez Sanchez Diego true true Diego González-Sánchez true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 120835663 /api/authorship/120835663 3 0.33333334 false true Author 10011745 /api/author/10011745 Szegedy Balázs true 10011745 true Balázs Szegedy true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PublicationIdentifier 27614716 /api/publicationidentifier/27614716 SwordSource 36 /api/publicationsource/36 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true REAL REAL http://real.mtak.hu/@@@ true true 36 true GREEN true 207266 http://real.mtak.hu/207266 false true PublicationIdentifier 27614552 /api/publicationidentifier/27614552 PlainSource 37 /api/publicationsource/37 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true arXiv http://arxiv.org/abs/@@@ true true 37 true IDENTICAL 2203.08915 http://arxiv.org/abs/2203.08915 false true /api/publication/35447049 <div class="PublicationOther Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <div class="autype autype0"> <span class="author-name" >Pablo Candela </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10076661"><a href="/gui2/?type=authors&mode=browse&sel=10076661" target="_blank">Diego González-Sánchez (<span class="authorship-author-name">Gonzalez Sanchez Diego</span> <span class="authorAux-mtmt"> </span>) </a> </span> <span class="author-affil"><span title="HUN-REN Alfréd Rényi Institute of Mathematics">HUN-REN RAMKI</span>/Artificial Intelligence</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10011745"><a href="/gui2/?type=authors&mode=browse&sel=10011745" target="_blank">Balázs Szegedy (<span class="authorship-author-name">Szegedy Balázs</span> <span class="authorAux-mtmt"> Csoport elmélet</span>) </a> </span> <span class="author-affil"><span title="HUN-REN Alfréd Rényi Institute of Mathematics">HUN-REN RAMKI</span>/Artificial Intelligence</span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;35447049" target="_blank">On Fω2-affine-exchangeable probability measures</a></div> <div class="description"> </div> <div class="country"> Country: <span class="pageLength">62 p.</span> <span class="publishedYear">(2024)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Language: English | </span> <span class="identifiers"> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="207266" target="_blank" href="http://real.mtak.hu/207266"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="2203.08915" target="_blank" href="http://arxiv.org/abs/2203.08915"> arXiv </a> </span> </span> <div class="mtid"><span class="long-pub-mtid">Publication: 35447049</span> | <span class="status-data status-ADMIN_APPROVED"> Admin approved </span> Core | <span class="type-subtype">Miscellaneous ( Publication in repository ) </span> | <span class="pub-category">Scientific</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="lastModified">Last Modified: 2024.12.03. 14:46 György Wolf (MTMT Központi admin) </div> <div class="lockedBy">Temporarily locked 2024.10.30. 15:44 Beáta Bavalicsné Kerekes (MTMT ellenőrzés admin5) Gusztáv Ladányi (MTMT API user, admin) </div> </div></div>