Power-law behavior and condensation phenomena in disordered urn models

Abstract

Abstract. We investigate equilibrium statistical properties of urn models with disorder. Two urn models are proposed; one belongs to the Ehrenfest class, and the other corresponds to the Monkey class. These models are introduced from the view point of the power-law behavior and randomness; it is clarified that quenched random parameters play an important role in generating power-law behavior. We evaluate the occupation probability P (k) with which an urn has k balls by using the concept of statistical physics of disordered systems. In the disordered urn model belonging to the Monkey class, we find that above critical density ρ c for a given temperature, condensation phenomenon occurs and the occupation probability changes its scaling behavior from an exponential-law to a heavy tailed power-law in large k regime. We also discuss an interpretation of our results for explaining of macro-economy, in particular, emergence of wealth differentials. Power-law behavior and condensation phenomena in disordered urn models 2

Formation of monopolies in a bipartite market

“…This phenomenon of a monopoly is also known as condensation in other fields, corresponding to one of two equivalent entities (brands in this case) growing and eliminating the other. It has been observed in previous works in economics (Arthur, 1990), Ising models in physics (Inoue & Ohkubo, 2008;Laciana, Gual, Kalmus, Oteiza-Aguirre, & Rovere, 2014), and opinion dynamics (Sznajd-Weron, 2000). Figure 3.…”

Statistical Mechanics of Human Resource Allocation: A Mathematical Modeling of Job-Matching in Labor Markets

“…This paper is organized as follows. In section 2, we briefly review our previous study on the urn model with disorder [13] and several remarkable properties of the model such as Bose-Einstein condensation. We also mention that the urn model cannot take into account the interactions between agents.…”

“…In this model, one can show that a sort of Bose condensation takes place. Hence, here we introduce the urn model with a disorder and explain several macroscopic properties according to the reference [13].…”

“…The occupation probability of the Monkey class urn model with disorder. This figure was taken from our previous paper[13].…”

A unified time scale for quantum chaotic regimes

“…In this sense, the KS-entropy represents a robust indicator in the field [6][7][8][9][10][11][12][13][14]. The coarse-graining of the quantum phase space, as a consequence of the Uncertainty Principle (UP), has an intimate relationship with quantum chaos time scales [15][16][17][18][19], and quantum extensions for the KS-entropy have been proposed [20][21][22].…”