Bulletin of the London Mathematical Society最新文献

{"title":"On the maximum likelihood degree of Gaussian graphical models","authors":"Carlos Améndola,&nbsp;Rodica Andreea Dinu,&nbsp;Mateusz Michałek,&nbsp;Martin Vodička","doi":"10.1112/blms.70507","DOIUrl":"https://doi.org/10.1112/blms.70507","url":null,"abstract":"<p>In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML-degree behaves monotonically on induced subgraphs. Furthermore, we complete a missing argument that the ML-degree of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mi>th</mi>\u0000 </mrow>\u0000 <annotation>$n{rm th}$</annotation>\u0000 </semantics></math> cycle is larger than 1 for any <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 4$</annotation>\u0000 </semantics></math>, therefore completing the characterization that the only Gaussian graphical models with rational maximum likelihood estimator are the ones corresponding to chordal (decomposable) graphs. Finally, we prove that the formula for the ML-degree of a cycle conjectured by Drton, Sturmfels and Sullivant provides a correct lower bound.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70507","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149048032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the convergence of boundary points for hyperbolic inner functions","authors":"Anna Jové,&nbsp;Mateo Mencía","doi":"10.1112/blms.70506","DOIUrl":"https://doi.org/10.1112/blms.70506","url":null,"abstract":"<p>Given a hyperbolic inner function <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <mi>D</mi>\u0000 <mo>→</mo>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$ fcolon mathbb {D}rightarrow mathbb {D}$</annotation>\u0000 </semantics></math> with Denjoy–Wolff point <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>∈</mo>\u0000 <mi>∂</mi>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$ pin partial mathbb {D}$</annotation>\u0000 </semantics></math>, it is well-known that almost every point <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ζ</mi>\u0000 <mo>∈</mo>\u0000 <mi>∂</mi>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$ zeta in partial mathbb {D}$</annotation>\u0000 </semantics></math> converges to <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$ p$</annotation>\u0000 </semantics></math> under iteration of the radial extension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>f</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <mo>:</mo>\u0000 <mi>∂</mi>\u0000 <mi>D</mi>\u0000 <mo>→</mo>\u0000 <mi>∂</mi>\u0000 <mi>D</mi>\u0000 </mrow>\u0000 <annotation>$ f^*colon partial mathbb {D}rightarrow partial mathbb {D}$</annotation>\u0000 </semantics></math>. We provide explicit bounds for the rate of this convergence in terms of the angular derivative, holding almost surely. Our results also cover the case where the Denjoy–Wolff point is a singularity.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148981423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A tropical version of Martens' theorem for metric graphs","authors":"Giusi Capobianco,&nbsp;Angelina Zheng","doi":"10.1112/blms.70505","DOIUrl":"https://doi.org/10.1112/blms.70505","url":null,"abstract":"<p>We study the conjecture stated by Jensen and Len on a tropical version on Martens' theorem via the Brill–Noether rank of a tropical curve. We recall Coppens' counterexample of Martens-special chain of cycles, and we generalize the construction defining another class of graphs, Martens-special trees of cycles, for which the conjecture does not hold in a similar setting. These are not the only counterexamples. However, we prove that the conjecture holds for all metric graphs with a stricter assumption on the degree in the Brill–Noether rank.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70505","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148981469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On locally distinguishing Sierpiński dynamical systems","authors":"Sergei Merenkov","doi":"10.1112/blms.70502","DOIUrl":"https://doi.org/10.1112/blms.70502","url":null,"abstract":"<p>We prove that there is no local quasiconformal map between the limit set of a convex-cocompact Kleinian group and the Julia set of a postcritically finite rational map, provided that both are Sierpiński carpets. This contrasts with the recent results by Y. Luo, D. Ntalampekos and Y. Luo, M. Mj, S. Mukherjee for gasket and tree-like spaces, respectively.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148981470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Torsors under the Jacobians of the universal Fermat curves","authors":"Qixiao Ma","doi":"10.1112/blms.70503","DOIUrl":"https://doi.org/10.1112/blms.70503","url":null,"abstract":"<p>Fix an integer <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$mgeqslant 3$</annotation>\u0000 </semantics></math>. Let us consider the universal family of degree-<span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> Fermat curves over <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbb {C}$</annotation>\u0000 </semantics></math>. For the whole family, we show that every torsor of the relative Jacobian is necessarily isomorphic to a connected component of the relative Picard scheme. For the generic fiber, we show that the Jacobian admits uncountably many nonisomorphic torsors.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148981471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exponential convergence for ultrafast diffusion equations with log-concave weights","authors":"Max Fathi,&nbsp;Mikaela Iacobelli","doi":"10.1112/blms.70472","DOIUrl":"https://doi.org/10.1112/blms.70472","url":null,"abstract":"<p>We study the asymptotic behavior of a weighted ultrafast diffusion PDE on the real line, with a log-concave and log-lipschitz weight, and prove exponential convergence to equilibrium. This result goes beyond the compact setting studied in Iacobelli [Discrete Contin. Dyn. Syst. <b>39</b> (2019), 4929–4943]. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in Caglioti, Golse, and Iacobelli [Math. Models Methods Appl. Sci. <b>25</b> (2015), 1845–1885].</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70472","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148942434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Refinements on higher order Weil–Oesterlé bounds via a Serre type argument","authors":"Emmanuel Hallouin,&nbsp;Philippe Moustrou,&nbsp;Marc Perret","doi":"10.1112/blms.70483","DOIUrl":"https://doi.org/10.1112/blms.70483","url":null,"abstract":"<p>Weil's theorem gives the most standard bound on the maximum number of points <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>g</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$N_q(g)$</annotation>\u0000 </semantics></math> of a curve of genus <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> over a finite field <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 <annotation>$mathbb {F}_q$</annotation>\u0000 </semantics></math>. This bound was improved by Ihara and Oesterlé for larger genus. A recent point of view allows one to recover these bounds by solving a sequence of semi-definite programs, and the first two steps lead to Weil's and Ihara's bounds. Another refinement of Weil's bound was obtained by Serre, involving arithmetic constraints. In this article, we combine these two approaches and propose a strengthening of Ihara's bound, based on an argument similar to Serre's refinement. We obtain a closed formula that generically improves upon Ihara's bound, even in the range where it was the best explicit bound so far. This provides new upper bounds on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>g</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$N_q(g)$</annotation>\u0000 </semantics></math> for infinitely many pairs <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>q</mi>\u0000 <mo>,</mo>\u0000 <mi>g</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(q,g)$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70483","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148943634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The pseudoautomorphism group of \u0000 \u0000 \u0000 P\u0000 3\u0000 \u0000 $mathbb {P}^3$\u0000 blown-up at 8 very general points","authors":"Cécile Gachet","doi":"10.1112/blms.70475","DOIUrl":"https://doi.org/10.1112/blms.70475","url":null,"abstract":"<p>We prove that the pseudoautomorphism group of a blow-up of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^3$</annotation>\u0000 </semantics></math> at 8 very general points is trivial. We also establish the injectivity of the Coble representation associated to blow-ups of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^3$</annotation>\u0000 </semantics></math> at <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>⩾</mo>\u0000 <mn>8</mn>\u0000 </mrow>\u0000 <annotation>$rgeqslant 8$</annotation>\u0000 </semantics></math> general points, answering a question of Dolgachev–Ortland.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148943641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The derived depth formula for modules of finite quasi-projective dimension","authors":"Luigi Ferraro,&nbsp;Justin Lyle","doi":"10.1112/blms.70491","DOIUrl":"https://doi.org/10.1112/blms.70491","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mi>k</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(R,mathfrak {m},mathbb {k})$</annotation>\u0000 </semantics></math> be a commutative Noetherian local ring. We prove a variety of new formulas for modules of finite quasi-projective or finite quasi-injective dimension. These include the Derived Depth Formula, itself an extension of Auslander's famous depth formula, a variation of the Derived Depth Formula for width, an extended version of Ischebeck's Formula, and a Dependency formula in the vein of Jorgensen. Several special cases of our main results are new even under stronger assumptions on the vanishing of various complete intersection dimensions.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148848999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Invariant measures and traces on groupoid \u0000 \u0000 \u0000 C\u0000 *\u0000 \u0000 ${mathrm{C}^ast }$\u0000 -algebras","authors":"Alistair Miller,&nbsp;Eduardo Scarparo","doi":"10.1112/blms.70492","DOIUrl":"https://doi.org/10.1112/blms.70492","url":null,"abstract":"<p>We provide sufficient conditions for the existence of a trace on the essential <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <annotation>$mathrm{C}^ast$</annotation>\u0000 </semantics></math>-algebra of a (not necessarily Hausdorff) étale groupoid <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> which extends an invariant measure <span></span><math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> on the unit space of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. In particular, it suffices for the isotropy groups of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> to be amenable, or for <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> to be essentially free with respect to <span></span><math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math>. We also show that <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is essentially free with respect to an invariant measure <span></span><math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> if and only if <span></span><math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> extends to a unique trace on the full <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <annotation>$mathrm{C}^ast$</annotation>\u0000 </semantics></math>-algebra of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. We work in the generality of possibly infinite measures and, accordingly, possibly unbounded traces. Moreover, whenever possible, we state our results for twisted groupoids. As an application, we show that gauge-invariant algebras of finite-state self-similar groups admit a unique tracial state.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"58 9","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148848964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}