S. S. Manna

Pareto law in a kinetic model of market with random saving propensity

We have numerically simulated the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving two-body collision. Unlike in the ideal gas, we introduce (quenched) saving propensity of the agents, distributed widely between the agents (0⩽λ<1). The system remarkably self-organizes to a critical Pareto distribution of money P(m)∼m−(ν+1) with ν≃1. We analyze the robustness (universality) of the distribution in the model. We also argue that although the fractional saving ingredient is a bit unnatural one in the context of gas models, our model is the simplest so far, showing self-organized criticality, and combines two century-old distributions: Gibbs (1901) and Pareto (1897) distributions.

Two-state model of self-organized criticality

Studies a two-state version of the sandpile model of self-organized criticality. Instead of a critical height of stability as in the sandpile model, the author introduces a hard core repulsion among different particles at the same position. In the case of a collision particles hop randomly to the nearest neighbours. Critical exponents obtained by numerical simulation show strong disagreement with the values theoretically predicted for the sandpile model but they are close to the numerical values of other models.

Large-scale simulation of avalanche cluster distribution in sand pile model

The avalanche cluster distribution of the sand pile model of self-organized criticality is studied on the square lattice. A vectorized multispin coding algorithm is developed for this study with three bits per site. The exponents characterizing the size and the lifetime of the avalanches are slightly different from the previous estimates.

Modulated scale-free network in Euclidean space

A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its ith predecessor of degree k(i) with a directed link of length l using a probability proportional to k(i)l(alpha). Our numerical study indicates that the network is scale free for all values of alpha>alpha(c) and the degree distribution decays stretched exponentially for the other values of alpha. The link length distribution follows a power law: D(l) approximately l(delta), where delta is calculated exactly for the whole range of values of alpha.

Money in gas-like markets: Gibbs and Pareto laws

We consider the ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, we introduce saving propensity

Critical exponents of the sand pile models in two dimensions

\lambda

Phase transition in a directed traffic flow network

of agents, such that each agent saves a fraction

Scale-free networks from a Hamiltonian dynamics

\lambda

Precise determination of the fractal dimensions of Apollonian packing and space-filling bearings

of its money and trades with the rest. We show the steady-state money or wealth distribution in a market is Gibbs-like for

A new route to Explosive Percolation

\lambda=0