799 research outputs found
Invariance principles for random bipartite planar maps
Random planar maps are considered in the physics literature as the discrete
counterpart of random surfaces. It is conjectured that properly rescaled random
planar maps, when conditioned to have a large number of faces, should converge
to a limiting surface whose law does not depend, up to scaling factors, on
details of the class of maps that are sampled. Previous works on the topic,
starting with Chassaing and Schaeffer, have shown that the radius of a random
quadrangulation with faces, that is, the maximal graph distance on such a
quadrangulation to a fixed reference point, converges in distribution once
rescaled by to the diameter of the Brownian snake, up to a scaling
constant. Using a bijection due to Bouttier, Di Francesco and Guitter between
bipartite planar maps and a family of labeled trees, we show the corresponding
invariance principle for a class of random maps that follow a Boltzmann
distribution putting weight on faces of degree : the radius of such
maps, conditioned to have faces (or vertices) and under a criticality
assumption, converges in distribution once rescaled by to a scaled
version of the diameter of the Brownian snake. Convergence results for the
so-called profile of maps are also provided. The convergence of rescaled
bipartite maps to the Brownian map, in the sense introduced by Marckert and
Mokkadem, is also shown. The proofs of these results rely on a new invariance
principle for two-type spatial Galton--Watson trees.Comment: Published in at http://dx.doi.org/10.1214/009117906000000908 the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Scaling limits of random planar maps with large faces
We discuss asymptotics for large random planar maps under the assumption that
the distribution of the degree of a typical face is in the domain of attraction
of a stable distribution with index . When the number of
vertices of the map tends to infinity, the asymptotic behavior of distances
from a distinguished vertex is described by a random process called the
continuous distance process, which can be constructed from a centered stable
process with no negative jumps and index . In particular, the profile
of distances in the map, rescaled by the factor , converges to
a random measure defined in terms of the distance process. With the same
rescaling of distances, the vertex set viewed as a metric space converges in
distribution as , at least along suitable subsequences, toward a
limiting random compact metric space whose Hausdorff dimension is equal to
.Comment: Published in at http://dx.doi.org/10.1214/10-AOP549 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - II. Implementation Issues
The idea of iterative process optimization based on collected output
measurements, or "real-time optimization" (RTO), has gained much prominence in
recent decades, with many RTO algorithms being proposed, researched, and
developed. While the essential goal of these schemes is to drive the process to
its true optimal conditions without violating any safety-critical, or "hard",
constraints, no generalized, unified approach for guaranteeing this behavior
exists. In this two-part paper, we propose an implementable set of conditions
that can enforce these properties for any RTO algorithm. This second part
examines the practical side of the sufficient conditions for feasibility and
optimality (SCFO) proposed in the first and focuses on how they may be enforced
in real application, where much of the knowledge required for the conceptual
SCFO is unavailable. Methods for improving convergence speed are also
considered.Comment: 56 pages, 15 figure
Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - I. Theoretical Foundations
The idea of iterative process optimization based on collected output
measurements, or "real-time optimization" (RTO), has gained much prominence in
recent decades, with many RTO algorithms being proposed, researched, and
developed. While the essential goal of these schemes is to drive the process to
its true optimal conditions without violating any safety-critical, or "hard",
constraints, no generalized, unified approach for guaranteeing this behavior
exists. In this two-part paper, we propose an implementable set of conditions
that can enforce these properties for any RTO algorithm. The first part of the
work is dedicated to the theory behind the sufficient conditions for
feasibility and optimality (SCFO), together with their basic implementation
strategy. RTO algorithms enforcing the SCFO are shown to perform as desired in
several numerical examples - allowing for feasible-side convergence to the
plant optimum where algorithms not enforcing the conditions would fail.Comment: Working paper; supplementary material available at:
http://infoscience.epfl.ch/record/18807
Diboson resonances within a custodially protected warped extra-dimensional scenario
We propose an interpretation of the diboson excess recently observed by the
ATLAS and CMS collaborations in terms of Kaluza-Klein excitations of
electroweak gauge bosons stemming from a realization of a warped
extra-dimensional model that is protected by a custodial symmetry. Besides
accounting for the LHC diboson data, this scenario also leads to an explanation
of the anomalies that have been observed in the measurements of the
forward-backward asymmetries for bottom quarks at LEP and top quarks at the
Tevatron.Comment: 10 pages, 2 figure
Strong Isotopic Effect in Phase II of Dense Solid Hydrogen and Deuterium
Quantum nuclear zero-point motions in solid H and D under pressure
are investigated at 80 K up to 160 GPa by first-principles path-integral
molecular dynamics calculations. Molecular orientations are well-defined in
phase II of D, while solid H exhibits large and very asymmetric angular
quantum fluctuations in this phase, with possible rotation in the (bc) plane,
making it difficult to associate a well-identified single classical structure.
The mechanism for the transition to phase III is also described. Existing
structural data support this microscopic interpretation.Comment: 5 pages, 3 figure
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