arXiv subjects
Publications and source records attributed to Wataru Souma.
We report empirical studies on the personal income distribution, and clarify that the distribution pattern of the lognormal with power law tail is the universal structure. We analyze the temporal change of Pareto index and Gibrat index to investigate the change of the inequality of the income distribution. In addition some mathematical models which are proposed to explain the power law distribution are reviewed.
We discuss the phase structure of the four-dimensional compact U(1) gauge theory at finite temperature using a deformation of the topological model. Its phase structure can be determined by the behavior of the Coulomb gas (CG) system on the cylinder. We utilize the relation between the CG system and the sine-Gordon (SG) model, and investigate the phase structure of the gauge theory in terms of the SG model. Especially, the critical-line equation of the gauge theory in the strong-coupling and high-temperature region is obtained by calculating the one-loop effective potential of the SG model.
We construct a model of wealth distribution, based on an interactive multiplicative stochastic process on static complex networks. Through numerical simulations we show that a decrease in the number of links discourages equality in wealth distribution, while the rewiring of links in small-world networks encourages it. Inequal distributions obey log-normal distributions, which are produced by wealth clustering. The rewiring of links breaks the wealth clustering and makes wealth obey the mean field type (power law) distributions. A mechanism that explains the appearance of log-normal distributions with a power law tail is proposed.
We investigate the Japanese personal income distribution in the high income range over the 112 years 1887-1998, and that in the middle income range over the 44 years 1955-98. It is observed that the distribution pattern of the lognormal with power law tail is the universal structure. However the indexes specifying the distribution differ from year to year. One of the index characterizing the distribution is the mean value of the lognormal distribution; the mean income in the middle income range. It is found that this value correlates linearly with the Gross Domestic Product (GDP). To clarify the temporal change of the equality or inequality of the distribution, we analyze Pareto and Gibrat indexes, which characterize the distribution in the high income range and that in the middle income range respectively. It is found for some years that there is no correlation between the high income and the middle income. It is also shown that the mean value of Pareto index equals to 2, and the change of this index is effected by the change of the asset price. From these analysis we derive four constraints that must be satisfied by mathematical models.
The exact renormalization group equation for pure quantum gravity is derived for an arbitrary gauge parameter in the space-time dimension $d=4$. This equation is given by a non-linear functional differential equation for the effective average action. An action functional of the effective average action is approximated by the same functional space of the Einstein-Hilbert action. From this approximation, $β$-functions for the dimensionless Newton constant and cosmological constant are derived non-perturbatively. These are used for an analysis of the phase structure and the ultraviolet non-Gaussian fixed point of the dimensionless Newton constant. This fixed point strongly depends on the gauge parameter and the cutoff function. However, this fixed point exists without these ambiguities, except for some gauges. Hence, it is possible that pure quantum gravity in $d=4$ is an asymptotically safe theory and non-perturbatively renormalizable.
We analyze the distribution of income and income tax of individuals in Japan for the fiscal year 1998. From the rank-size plots we find that the accumulated probability distribution of both data obey a power law with a Pareto exponent very close to -2. We also present an analysis of the distribution of the debts owed by bankrupt companies from 1997 to March, 2000, which is consistent with a power law behavior with a Pareto exponent equal to -1. This power law is the same as that of the income distribution of companies. Possible implications of these findings for model building are discussed.
The cutoff scheme dependence in the several formulations of the Exact Renormalization Group (ERG) is investigated. It is shown that the cutoff scheme dependence of the Wilsonian effective action is regarded as a certain coordinate transformation on the theory space. From this observation the Wilsonian effective actions are found to suffer from strong dependence on the schemes even in the infra-red asymptotic region for massive theories. However there is no such scheme dependence in the one particle irreducible parts of them, which is called the effective average actions. We also derive the explicit form of the Polchinski RG equation in the sharp cutoff limit. Finally this equation is shown to be identical with the Wegner-Houghton RG equation.
The non-trivial ultraviolet fixed point in quantum gravity is calculated by means of the exact renormalization group equation in d-dimensions $(2\simeq d\leq4)$. It is shown that the ultraviolet non-Gaussian fixed point which is expected from the perturbatively $ε$-expanded calculations in $2+ε$ gravity theory remains in d=4. Hence it is possible that quantum gravity is an asymptotically safe theory and renormalizable in 2<d.
The truncation scheme dependence of the exact renormalization group equations is investigated for scalar field theories in three dimensions. The exponents are numerically estimated to the next-to-leading order of the derivative expansion. It is found that the convergence property in various truncations in the number of powers of the fields is remarkably improved if the expansion is made around the minimum of the effective potential. It is also shown that this truncation scheme is suitable for evaluation of infrared effective potentials. The physical interpretation of this improvement is discussed by considering O(N) symmetric scalar theories in the large-N limit.
The non-perturbative Wegner-Houghton renormalization group is analyzed by the local potential approximation in O(N) scalar theories in d-dimensions $(3\leq d\leq 4)$. The leading critical exponents νare calculated in order to investigate the effectiveness of the local potential approximation by comparing them with the other non-perturbative methods. We show analytically that the local potential approximation gives the exact exponents up to $O(ε)$ in ε-expansion and the leading in 1/N-expansion. We claim that this approximation offers fairly accurate results in the whole range of the parameter space of N and d. It is a great advantage of our method that no diverging expansions appear in the procedure.