3,161 research outputs found
Regenerative tree growth: structural results and convergence
We introduce regenerative tree growth processes as consistent families of
random trees with n labelled leaves, n>=1, with a regenerative property at
branch points. This framework includes growth processes for exchangeably
labelled Markov branching trees, as well as non-exchangeable models such as the
alpha-theta model, the alpha-gamma model and all restricted exchangeable models
previously studied. Our main structural result is a representation of the
growth rule by a sigma-finite dislocation measure kappa on the set of
partitions of the natural numbers extending Bertoin's notion of exchangeable
dislocation measures from the setting of homogeneous fragmentations. We use
this representation to establish necessary and sufficient conditions on the
growth rule under which we can apply results by Haas and Miermont for
unlabelled and not necessarily consistent trees to establish self-similar
random trees and residual mass processes as scaling limits. While previous
studies exploited some form of exchangeability, our scaling limit results here
only require a regularity condition on the convergence of asymptotic
frequencies under kappa, in addition to a regular variation condition.Comment: 23 pages, new title, restructured, presentation improve
Validation of a mathematical model for road cycling power
Journal ArticleThis investigation sought to determine if cycling power could be accurately modeled. A mathematical model of cycling power was derived, and values for each model parameter were determined. A bicycle-mounted power measurement system was validated by comparison with a laboratory ergometer
Large N and the Dine-Rajaraman problem
We compute the effective action for scattering of three well-separated
extremal brane solutions, in 11d supergravity, with zero p_ transfer and small
transverse velocities. Using an interpretation of the conjecture of Maldacena,
following Hyun, this can be viewed as the large N limit of the Matrix theory
description of three supergraviton scattering at leading order. The result is
consistent with the perturbative supergravity calculation.Comment: 10 pages, tex (harvmac
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