281,637 research outputs found
Non-trivial linear bounds for a random walk driven by a simple symmetric exclusion process
Non-trivial linear bounds are obtained for the displacement of a random walk
in a dynamic random environment given by a one-dimensional simple symmetric
exclusion process in equilibrium. The proof uses an adaptation of multiscale
renormalization methods of Kesten and Sidoravicius.Comment: 20 pages, 3 figure
The exponential map is chaotic: An invitation to transcendental dynamics
We present an elementary and conceptual proof that the complex exponential
map is "chaotic" when considered as a dynamical system on the complex plane.
(This result was conjectured by Fatou in 1926 and first proved by Misiurewicz
55 years later.) The only background required is a first undergraduate course
in complex analysis.Comment: 22 pages, 4 figures. (Provisionally) accepted for publication the
American Mathematical Monthly. V2: Final pre-publication version. The article
has been revised, corrected and shortened by 14 pages; see Version 1 for a
more detailed discussion of further properties of the exponential map and
wider transcendental dynamic
Law of large numbers for non-elliptic random walks in dynamic random environments
We prove a law of large numbers for a class of -valued random walks in
dynamic random environments, including non-elliptic examples. We assume for the
random environment a mixing property called \emph{conditional cone-mixing} and
that the random walk tends to stay inside wide enough space-time cones. The
proof is based on a generalization of a regeneration scheme developed by Comets
and Zeitouni for static random environments and adapted by Avena, den Hollander
and Redig to dynamic random environments. A number of one-dimensional examples
are given. In some cases, the sign of the speed can be determined.Comment: 36 pages, 4 figure
Resonant cancellation of off-resonant effects in a multilevel qubit
Off-resonant effects are a significant source of error in quantum
computation. This paper presents a group theoretic proof that off-resonant
transitions to the higher levels of a multilevel qubit can be completely
prevented in principle. This result can be generalized to prevent unwanted
transitions due to qubit-qubit interactions. A simple scheme exploiting dynamic
pulse control techniques is presented that can cancel transitions to higher
states to arbitrary accuracy.Comment: 4 pages, Revtex, submitted for publicatio
Long and thin covers for flow spaces
Long and thin covers of flow spaces are important ingredients in the proof of
the Farrell--Jones conjecture for certain classes of groups, like hyperbolic
and CAT(0)-groups. In this paper we provide an alternative construction of such
covers which holds in a more general setting and simplifies some of the
arguments.Comment: 22 pages; the title no longer contains the word cocompact, some more
changes following a referee report; to appear in Groups, Geometry, and
Dynamic
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