6,119 research outputs found
Differential equation approximations for Markov chains
We formulate some simple conditions under which a Markov chain may be
approximated by the solution to a differential equation, with quantifiable
error probabilities. The role of a choice of coordinate functions for the
Markov chain is emphasised. The general theory is illustrated in three
examples: the classical stochastic epidemic, a population process model with
fast and slow variables, and core-finding algorithms for large random
hypergraphs.Comment: Published in at http://dx.doi.org/10.1214/07-PS121 the Probability
Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Structure of large random hypergraphs
The theme of this paper is the derivation of analytic formulae for certain
large combinatorial structures. The formulae are obtained via fluid limits of
pure jump type Markov processes, established under simple conditions on the
Laplace transforms of their Levy kernels. Furthermore, a related Gaussian
approximation allows us to describe the randomness which may persist in the
limit when certain parameters take critical values. Our method is quite
general, but is applied here to vertex identifiability in random hypergraphs. A
vertex v is identifiable in n steps if there is a hyperedge containing v all of
whose other vertices are identifiable in fewer than n steps. We say that a
hyperedge is identifiable if every one of its vertices is identifiable. Our
analytic formulae describe the asymptotics of the number of identifiable
vertices and the number of identifiable hyperedges for a Poisson random
hypergraph on a set of N vertices, in the limit as N goes to infinity.Comment: Revised version with minor conceptual improvements and additional
discussion. 32 pages, 5 figure
High-dimensional quantum dynamics of adsorption and desorption of H at Cu(111)
We performed high-dimensional quantum dynamical calculations of the
dissociative adsorption and associative desorption of hydrogen on Cu(111). The
potential energy surface (PES) is obtained from density functional theory
calculations. Two regimes of dynamics are found, at low energies sticking is
determined by the minimum energy barrier, at high energies by the distribution
of barrier heights. Experimental results are well-reproduced qualitatively, but
some quantitative discrepancies are identified as well.Comment: 4 two column pages, revtex, 4 figures, to appear in Phys. Rev. Let
Cosmological Bounds on Spatial Variations of Physical Constants
We derive strong observational limits on any possible large-scale spatial
variation in the values of physical 'constants' whose space-time evolution is
driven by a scalar field. The limits are imposed by the isotropy of the
microwave background on large angular scales in theories which describe space
and time variations in the fine structure constant, the electron-proton mass
ratio, and the Newtonian gravitational constant, G. Large-scale spatial
fluctuations in the fine structure constant are bounded by 2x10^-9 and
1.2x10^-8 in the BSBM and VSL theories respectively, fluctuations in the
electron-proton mass ratio by 9x10^-5 in the BM theory and fluctuations in G by
3.6x10^-10 in Brans-Dicke theory. These derived bounds are significantly
stronger than any obtainable by direct observations of astrophysical objects at
the present time.Comment: 13 pages, 1 table, typos corrected, refs added. Published versio
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