arXiv subjects

Jun Ohkubo

Publications and source records attributed to Jun Ohkubo.

58 records · Page 4Linked to original sources

arXiv2007

A field theoretic approach to master equations and a variational method beyond the Poisson ansatz

We develop a variational scheme in a field theoretic approach to a stochastic process. While various stochastic processes can be expressed using master equations, in general it is difficult to solve the master equations exactly, and it is also hard to solve the master equations numerically because of the curse of dimensionality. The field theoretic approach has been used in order to study such complicated master equations, and the variational scheme achieves tremendous reduction in the dimensionality of master equations. For the variational method, only the Poisson ansatz has been used, in which one restricts the variational function to a Poisson distribution. Hence, one has dealt with only restricted fluctuation effects. We develop the variational method further, which enables us to treat an arbitrary variational function. It is shown that the variational scheme developed gives a quantitatively good approximation for master equations which describe a stochastic gene regulatory network.

cond-mat.stat-mech↗

arXiv2007

Free energy of disordered urn models in the canonical ensemble

We calculate the free energy of the disordered urn model using the law of large numbers. It is revealed that the saddle point equation obtained by the usage of the law of large numbers is the same as that obtained by the replica method. Hence, we conclude that the replica symmetric solution is adequate for the disordered urn model. Furthermore, we point out the mathematical similarity of free energies between the urn models and the Random Field Ising Model; this similarity gives an evidence that the replica symmetric solution of the urn models is exact.

cond-mat.dis-nn↗

arXiv2006

Replica analysis of a preferential urn model

We analyse a preferential urn model with randomness using the replica method. The preferential urn model is a stochastic model based on the concept "the rich get richer." The replica analysis clarifies that the preferential urn model with randomness shows a fat-tailed occupation distribution. The analytical treatments and results would be useful for various research fields such as complex networks, stochastic models, and econophysics.

cond-mat.dis-nn↗

arXiv2005

Statistical-mechanical iterative algorithms on complex networks

The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a statistical-mechanical iterative algorithm is often used. We study the statistical-mechanical iterative algorithm on complex networks. To investigate effects of heterogeneous structures on the iterative algorithm, we introduce an iterative algorithm based on information of heterogeneity of complex networks, in which higher-degree nodes are likely to be updated more frequently than lower-degree ones. Numerical experiments clarified that the usage of the information of heterogeneity affects the algorithm in BA networks, but does not influence that in ER networks. It is revealed that information of the whole system propagates rapidly through such high-degree nodes in the case of Barab{á}si-Albert's scale-free networks.

cond-mat.dis-nn↗