313 research outputs found
Families of infinitely divisible distributions closed under mixing and convolution
Certain families of probability distribution functions maintain their infinite divisibility under repeated mixing and convolution. Examples on the continuum and lattice are given. The main tools used are Polya's criteria and the properties of log-convexity and complete monotonicity. Some light is shed on the relationship between these two properties
Coherent Diffusion of Polaritons in Atomic Media
Coherent diffusion pertains to the motion of atomic dipoles experiencing
frequent collisions in vapor while maintaining their coherence. Recent
theoretical and experimental studies on the effect of coherent diffusion on key
Raman processes, namely Raman spectroscopy, slow polariton propagation, and
stored light, are reviewed in this Colloquium.Comment: Submitted to Review of Modern Physic
Accuracy of one-dimensional collision integral in the rigid spheres approximation
The accuracy of calculation of spectral line shapes in one-dimensional
approximation is studied analytically in several limiting cases for arbitrary
collision kernel and numerically in the rigid spheres model. It is shown that
the deviation of the line profile is maximal in the center of the line in case
of large perturber mass and intermediate values of collision frequency. For
moderate masses of buffer molecules the error of one-dimensional approximation
is found not to exceed 5%.Comment: LaTeX, 24 pages, 8 figure
Metastates in mean-field models with random external fields generated by Markov chains
We extend the construction by Kuelske and Iacobelli of metastates in
finite-state mean-field models in independent disorder to situations where the
local disorder terms are are a sample of an external ergodic Markov chain in
equilibrium. We show that for non-degenerate Markov chains, the structure of
the theorems is analogous to the case of i.i.d. variables when the limiting
weights in the metastate are expressed with the aid of a CLT for the occupation
time measure of the chain. As a new phenomenon we also show in a Potts example
that, for a degenerate non-reversible chain this CLT approximation is not
enough and the metastate can have less symmetry than the symmetry of the
interaction and a Gaussian approximation of disorder fluctuations would
suggest.Comment: 20 pages, 2 figure
M/M/ queues in semi-Markovian random environment
In this paper we investigate an M/M/ queue whose parameters depend on
an external random environment that we assume to be a semi-Markovian process
with finite state space. For this model we show a recursive formula that allows
to compute all the factorial moments for the number of customers in the system
in steady state. The used technique is based on the calculation of the raw
moments of the measure of a bidimensional random set. Finally the case when the
random environment has only two states is deeper analyzed. We obtain an
explicit formula to compute the above mentioned factorial moments when at least
one of the two states has sojourn time exponentially distributed.Comment: 17 pages, 2 figure
An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci
A model of mutation rate evolution for multiple loci under arbitrary
selection is analyzed. Results are obtained using techniques from Karlin (1982)
that overcome the weak selection constraints needed for tractability in prior
studies of multilocus event models. A multivariate form of the reduction
principle is found: reduction results at individual loci combine topologically
to produce a surface of mutation rate alterations that are neutral for a new
modifier allele. New mutation rates survive if and only if they fall below this
surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994)
for a multilocus recombination modifier. Increases in mutation rates at some
loci may evolve if compensated for by decreases at other loci. The strength of
selection on the modifier scales in proportion to the number of germline cell
divisions, and increases with the number of loci affected. Loci that do not
make a difference to marginal fitnesses at equilibrium are not subject to the
reduction principle, and under fine tuning of mutation rates would be expected
to have higher mutation rates than loci in mutation-selection balance. Other
results include the nonexistence of 'viability analogous, Hardy-Weinberg'
modifier polymorphisms under multiplicative mutation, and the sufficiency of
average transmission rates to encapsulate the effect of modifier polymorphisms
on the transmission of loci under selection. A conjecture is offered regarding
situations, like recombination in the presence of mutation, that exhibit
departures from the reduction principle. Constraints for tractability are:
tight linkage of all loci, initial fixation at the modifier locus, and mutation
distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded
introductory and discussion sections, added corollaries, new results on
modifier polymorphisms, minor corrections. 49 pages, 64 reference
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