Journal: Transactions of the American Mathematical Society

Abbreviation

Trans. Amer. Math. Soc.

Publisher

American Mathematical Society

Journal Volumes

ISSN

1088-6850
0002-9947

Description

Filters

Reset filters

Search Results

Publications1 - 10 of 46
  • Markov random walks on homogeneous spaces and Diophantine approximation on fractals
    Item type: Journal Article
    Prohaska, Roland; Sert, Çagri (2020)
    Transactions of the American Mathematical Society
    In the first part, using the recent measure classification results of Eskin-Lindenstrauss, we give a criterion to ensure a.s. equidistribution of empirical measures of an i.i.d. random walk on a homogeneous space G/Γ. Employing renewal and joint equidistribution arguments, this result is generalized in the second part to random walks with Markovian dependence. Finally, following a strategy of Simmons-Weiss, we apply these results to Diophantine approximation problems on fractals and show that almost every point with respect to Hausdorff measure on a graph directed self-similar set is of generic type, so, in particular, well approximable. © 2020 American Mathematical Society.
  • Log-concavity properties of minkowski valuations
    Item type: Journal Article
    Berg, Astrid; Parapatits, Lukas; Schuster, Franz E.; et al. (2018)
    Transactions of the American Mathematical Society
  • Asymptotically rigid mapping class groups II: strand diagrams and non-positive curvature
    Item type: Journal Article
    Genevois, Anthony; Lonjou, Anne; Urech, Christian (2025)
    Transactions of the American Mathematical Society
    In this article, we introduce a new family of groups, called Chambord groups and constructed from braided strand diagrams associated to specific semigroup presentations. It includes the asymptotically rigid mapping class groups previously studied by the authors such as the braided Higman-Thompson groups and the braided Houghton groups. Our main result shows that polycyclic subgroups in Chambord groups are virtually abelian and undistorted.
  • Ramsey-Type Results For Semi-Algebraic Relations
    Item type: Journal Article
    Conlon, David; Fox, Jacob; Pach, Janos; et al. (2014)
    Transactions of the American Mathematical Society
  • Tower-type bounds for unavoidable patterns in words
    Item type: Journal Article
    Conlon, David; Fox, Jacob; Sudakov, Benny (2019)
    Transactions of the American Mathematical Society
  • Rolling backwards can move you forward: on embedding problems in sparse expanders
    Item type: Journal Article
    Draganic, Nemanja; Krivelevich, Michael; Nenadov, Rajko (2022)
    Transactions of the American Mathematical Society
    We develop a general embedding method based on the FriedmanPippenger tree embedding technique and its algorithmic version, enhanced with a roll-back idea allowing a sequential retracing of previously performed embedding steps. We use this method to obtain the following results. center dot We show that the size-Ramsey number of logarithmically long subdivisions of bounded degree graphs is linear in their number of vertices, settling a conjecture of Pak [Proceedings of the thirteenth annual ACMSIAM symposium on discrete algorithms (SODA'02), 2002, pp. 321328]. center dot We give a deterministic, polynomial time online algorithm for finding vertex-disjoint paths of a prescribed length between given pairs of vertices in an expander graph. Our result answers a question of Alon and Capalbo [48th annual IEEE symposium on foundations of computer science (FOCS'07), 2007, pp. 518-524]. center dot We show that relatively weak bounds on the spectral ratio lambda/d of dregular graphs force the existence of a topological minor of Kt where t = (1 - o(1))d. We also exhibit a construction which shows that the theoretical maximum t = d + 1 cannot be attained even if lambda = O( d). This answers a question of Fountoulakis, Ku spacing diaeresis hn and Osthus [Random Structures Algorithms 35 (2009), pp. 444-463].
  • On the explicit Torsion Anomalous Conjecture
    Item type: Journal Article
    Checcoli, Sara; Veneziano, Francesco; Viada, Evelina (2017)
    Transactions of the American Mathematical Society
  • Thresholds for latin squares and Steiner triple systems: Bounds within a logarithmic factor
    Item type: Journal Article
    Kang, Dong Yeap; Kelly, Tom; Kühn, Daniela; et al. (2023)
    Transactions of the American Mathematical Society
    We prove that for $n \in \mathbb N$ and an absolute constant $C$, if $p \geq C\log ^2 n / n$ and $L_{i,j} \subseteq [n]$ is a random subset of $[n]$ where each $k\in [n]$ is included in $L_{i,j}$ independently with probability $p$ for each $i, j\in [n]$, then asymptotically almost surely there is an order-$n$ Latin square in which the entry in the $i$th row and $j$th column lies in $L_{i,j}$. The problem of determining the threshold probability for the existence of an order-$n$ Latin square was raised independently by Johansson [Triangle factors in random graphs, 2006], by Luria and Simkin [Random Structures Algorithms 55 (2019), pp. 926–949], and by Casselgren and Häggkvist [Graphs Combin. 32 (2016), pp. 533–542]; our result provides an upper bound which is tight up to a factor of $\log n$ and strengthens the bound recently obtained by Sah, Sawhney, and Simkin [Threshold for Steiner triple systems, arXiv: 2204.03964, 2022]. We also prove analogous results for Steiner triple systems and $1$-factorizations of complete graphs, and moreover, we show that each of these thresholds is at most the threshold for the existence of a $1$-factorization of a nearly complete regular bipartite graph.
  • Rough path metrics on a Besov-Nikolskii-type scale
    Item type: Journal Article
    Friz, Peter K.; Prömel, David J. (2018)
    Transactions of the American Mathematical Society
  • On the solvability of singular Liouville equations on compact surfaces of arbitrary genus
    Item type: Journal Article
    Carlotto, Alessandro (2014)
    Transactions of the American Mathematical Society
Publications1 - 10 of 46