6,144 research outputs found
The boundary coefficient : a vertex measure for visualizing and finding structure in weighted graphs
Comment: The Need for Syncretism in Applied Statistics
Comment on "The Need for Syncretism in Applied Statistics" [arXiv:1012.1161]Comment: Published in at http://dx.doi.org/10.1214/10-STS308A the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Anyonic entanglement renormalization
We introduce a family of variational ansatz states for chains of anyons which
optimally exploits the structure of the anyonic Hilbert space. This ansatz is
the natural analog of the multi-scale entanglement renormalization ansatz for
spin chains. In particular, it has the same interpretation as a coarse-graining
procedure and is expected to accurately describe critical systems with
algebraically decaying correlations. We numerically investigate the validity of
this ansatz using the anyonic golden chain and its relatives as a testbed. This
demonstrates the power of entanglement renormalization in a setting with
non-abelian exchange statistics, extending previous work on qudits, bosons and
fermions in two dimensions.Comment: 19 pages, 10 figures, v2: extended, updated to match published
versio
Progress in noncommutative function theory
In this expository paper we describe the study of certain non-self-adjoint
operator algebras, the Hardy algebras, and their representation theory. We view
these algebras as algebras of (operator valued) functions on their spaces of
representations. We will show that these spaces of representations can be
parameterized as unit balls of certain -correspondences and the
functions can be viewed as Schur class operator functions on these balls. We
will provide evidence to show that the elements in these (non commutative)
Hardy algebras behave very much like bounded analytic functions and the study
of these algebras should be viewed as noncommutative function theory
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