arXiv subjects

Masashi Tomoyose

Publications and source records attributed to Masashi Tomoyose.

7 recordsLinked to original sources

arXiv2008

Non-Gibrat's law in the middle scale region

By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the equation which gives the Pareto index $μ$ in TST model. Moreover, we extend the model modifying the stochastic coefficient under a Non-Gibrat's law. In this model, the detailed balance is also numerically observed. The resultant pdf is power-law in the large scale Gibrat's law region, and is the log-normal distribution in the middle scale Non-Gibrat's one. These are accurately confirmed in the numerical simulation.

physics.soc-ph↗

arXiv2003

Fractal Structure with a Typical Scale

In order to understand characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce a concept of typical scale. We employ a model of 2d gravity modified by the $R^2$ term as a tool to understand such distributions through the typical scale. This model is obtained by adding an interaction term with a typical scale to a scale invariant system. A distribution derived in the model provides power law one in the large scale region, but Weibull-like one in the small scale region. As examples of distributions which have both fractal and non-fractal regions, we take those of personal income and citation number of scientific papers. We show that these distributions are fitted fairly well by the distribution curves derived analytically in the $R^2$ 2d gravity model. As a result, we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way. We also point out that the $R^2$ 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way.

cond-mat.stat-mech↗

arXiv2002

A New Approach to Personal Income Distribution

The results of R^2 dynamical random surface model (2-dimensional quantum gravity with a $R^2$ term) are applied to explain the personal income distribution. A scale invariance exists if there is not the $R^2$ term in the action. The R^2 term provides a typical scale and breaks the scale invariance explicitly in the low and middle income range. A new distribution, Weibull distribution, is deduced from the action analytically in the low income range, and a consistent fitting is obtained in the whole income range. Also, we show that the lognormal distribution in the middle income range can be understood in this framework.

cond-mat.stat-mech↗

arXiv2000

Non-ladder Extended Renormalization Group Analysis of the Dynamical Chiral Symmetry Breaking

The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the Non-Perturbative Renormalization Group (NPRG) equations. We employ an approximation scheme beyond ``the ladder'', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced compared with the ladder ones, which is phenomenologically favorable. The gauge dependence of the order parameters is fairly reduced in this scheme.

hep-th↗

arXiv1999

Analysis of the Wilsonian Effective Potentials in Dynamical Chiral Symmetry Breaking

The non-perturbative renormalization group equation for the Wilsonian effective potential is given in a certain simple approximation scheme in order to study chiral symmetry breaking phenomena dynamically induced by strong gauge interactions. The evolving effective potential is found to be non-analytic in infrared, which indicates spontaneous generation of the fermion mass. It is also shown that the renormalization group equation gives the identical effective fermion mass with that obtained by solving the Schwinger-Dyson equation in the (improved) ladder approximation. Moreover introduction of the collective field corresponding to the fermion composite into the theory space is found to offer an efficient method to evaluate the order parameters; the dynamical mass and the chiral condensate. The relation between the renormalization group equation incorporating the collective field and the Schwinger-Dyson equation is also clarified.

hep-th↗

arXiv1999

Wilson Renormalization Group Equations for the Critical Dynamics of Chiral Symmetry

The critical dynamics of the chiral symmetry breaking induced by gauge interaction is examined in the Wilson renormalization group framework in comparison with the Schwinger-Dyson approach. We derive the beta functions for the four-fermi couplings in the sharp cutoff renormalzation group scheme, from which the critical couplings and the anomalous dimensions of the fermion composite operators near criticality are immediately obtained. It is also shown that the beta functions lead to the same critical behavior found by solving the so-called ladder Schwinger-Dyson equation, if we restrict the radiative corrections to a certain limited type.

hep-th↗

arXiv1997

Non-Perturbative Renormalization Group Analysis of the Chiral Critical Behaviors in QED

We study the chiral critical behaviors of QED by using Non-Perturbative Renormalization Group (NPRG). Taking account of the non-ladder contributions, our flow equations are free from the gauge parameter ($α$) dependence. We clarify the chiral phase structure, and calculate the anomalous dimension of $\barψψ$, which is enhanced compared to the ladder approximation. We find that the cutoff scheme dependence of the physical results is very small.

hep-ph↗