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Now showing items 3301-3310 of 4210
Connective constants and height functions for Cayley graphs
(American Mathematical SocietyTransactions of the American Mathematical Society, 2017-03-31)
The connective constant $μ$($G$) of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved ...
Infinite loop spaces and positive scalar curvature
(SpringerInventiones Mathematicae, 2017-09-01)
We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there are no harmonic spinors on a manifold with positive scalar curvature ...
Four-Dimensional Weakly Self-avoiding Walk with Contact Self-attraction
(SpringerJournal of Statistical Physics, 2017-04-01)
We consider the critical behaviour of the continuous-time weakly self-avoiding walk with contact self-attraction on $\mathbb{Z}$$^{4}$, for sufficiently small attraction. We prove that the susceptibility and correlation ...
Random-projection ensemble classification
We introduce a very general method for high-dimensional classification, based on careful combination of the results of applying an arbitrary base classifier to random projections of the feature vectors into a lower-dimensional ...
Homological stability for moduli spaces of high dimensional manifolds. II
We prove a homological stability theorem for moduli spaces of manifolds
of dimension 2$\textit{n}$, for attaching handles of index at least $\textit{n}$, after these manifolds have been stabilised by countably many copies ...
Undecidability and the developability of permutoids and rigid pseudogroups
(Cambridge University PressForum of Mathematics, Sigma, 2017-03-20)
A $\textit{permutoid}$ is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there ...
Radically filtered quasi-hereditary algebras and rigidity of tilting modules
(Cambridge University PressMathematical Proceedings of the Cambridge Philosophical Society, 2017-09)
Let $\textit{A}$ be a quasi-hereditary algebra. We prove that in many cases, a tilting module is rigid (i.e. has identical radical and socle series) if it does not have certain subquotients whose composition factors extend ...
Teichmüller spaces and bounded symmetric domains do not mix isometrically
(SpringerGeometric and Functional Analysis, 2017-06-01)
This paper shows that, in dimensions two or more, there are no holomorphic isometries between Teichüller spaces and bounded symmetric domains in their intrinsic Kobayashi metric.
Elliptic curves over Q$_{∞}$ are modular
We show that if $\textit{p}$ is a prime, then all elliptic curves de ned over the cyclotomic $\mathbb{Z}$$_{p}$-extension of Q are modular.
Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees
We establish existence and uniqueness for Gaussian free field flow lines started at interior points of a planar domain. We interpret these as rays of a random geometry with imaginary curvature and describe the way distinct ...