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 $T$, 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 $F$ of the ancient nuclear DNA persists. We compute both $T$ and $F$. 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