417 research outputs found
Bethe-Peierls Approximation for the 2D Random Ising Model
The partition function of the 2d Ising model with random nearest neighbor
coupling is expressed in the dual lattice made of square plaquettes. The dual
model is solved in the the mean field and in different types of Bethe-Peierls
approximations, using the replica method.Comment: Plane TeX file, 21 pages, 5 figures available under request to
[email protected]
Mitochondrial Dna Replacement Versus Nuclear Dna Persistence
In this paper we consider two populations whose generations are not
overlapping and whose size is large. The number of males and females in both
populations is constant. Any generation is replaced by a new one and any
individual has two parents for what concerns nuclear DNA and a single one (the
mother) for what concerns mtDNA. Moreover, at any generation some individuals
migrate from the first population to the second.
In a finite random time , the mtDNA of the second population is completely
replaced by the mtDNA of the first. In the same time, the nuclear DNA is not
completely replaced and a fraction of the ancient nuclear DNA persists. We
compute both and . Since this study shows that complete replacement of
mtDNA in a population is compatible with the persistence of a large fraction of
nuclear DNA, it may have some relevance for the Out of Africa/Multiregional
debate in Paleoanthropology
Constrained annealing for spin glasses
The quenched free energy of spin glasses is estimated by means of annealed
averages where the frustration is constrained to its average value. We discuss
the case of d-dimensional Ising models with random nearest neighbour coupling,
and we introduce a new method to obtain constrained annealed averages without
recurring to Lagrange multipliers. It requires to perform quenched averages
either on small volumes in an analytic way, or on finite size strips via
products of random transfer matrices. We thus give a sequence of converging
lower bounds for the quenched free energy of 2d spin glasses.Comment: plane TeX file,24 pages. 6 figures may be requested to Paladin at
vxscaq.aquila.infn.i
Optimal Strategies for Prudent Investors
We consider a stochastic model of investment on an asset of a stock market
for a prudent investor. She decides to buy permanent goods with a fraction \a
of the maximum amount of money owned in her life in order that her economic
level never decreases. The optimal strategy is obtained by maximizing the
exponential growth rate for a fixed \a. We derive analytical expressions for
the typical exponential growth rate of the capital and its fluctuations by
solving an one-dimensional random walk with drift.Comment: 14 pages, LaTeX, epsfig.sty, 7 eps figures, minor changes; accepted
for International J. of Theoretical and Applied Financ
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