Antipersistent dynamics in kinetic models of wealth exchange

Goswami, Sanchari; Chatterjee, Arnab; Sen, Parongama

doi:10.1103/physreve.84.051118

Cited by 5 publications

(10 citation statements)

References 38 publications

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“…For financial data, a random walk picture was introduced as early as in 1900 by Louis Bachelier [13]. Later, similar walks were studied for mod-00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 00 00 11 11 0 0 1 1 0 0 0 1 1 1 els of wealth exchange [14,15].…”

Section: Introductionmentioning

confidence: 99%

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Virtual walks in spin space: A study in a family of two-parameter models

Mullick¹,

Sen²

2018

Phys. Rev. E

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We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalized two-parameter family of spin models characterized by parameters y and z [de Oliveira et al., J. Phys. A 26, 2317 (1993)JPHAC50305-447010.1088/0305-4470/26/10/006]. The behavior of S(x,t), the probability that the walker is at position x at time t, is studied in detail. In general S(x,t)∼t^{-α}f(x/t^{α}) with α≃1 or 0.5 at large times depending on the parameters. In particular, S(x,t) for the point y=1,z=0.5 corresponding to the Voter model shows a crossover in time; associated with this crossover, two timescales can be defined which vary with the system size L as L^{2}logL. We also show that as the Voter model point is approached from the disordered regions along different directions, the width of the Gaussian distribution S(x,t) diverges in a power law manner with different exponents. For the majority Voter case, the results indicate that the the virtual walk can detect the phase transition perhaps more efficiently compared to other nonequilibrium methods.

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Section: Introductionmentioning

confidence: 99%

“…For financial data, a random walk picture was introduced as early as in 1900 by Louis Bachelier [13]. Later, similar walks were studied for mod-00 00 11 els of wealth exchange [14,15].…”

Section: Introductionmentioning

confidence: 99%

Virtual walks in spin space: A study in a family of two-parameter models

Mullick¹,

Sen²

2018

Phys. Rev. E

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“…It is well known that the usual CCM walk can be compared to a biased random walk (BRW) whose forward bias decreases as we increase λ from zero. The walk has no bias at a particular λk=0.469 and then it decreases further and becomes negative on increasing λk [45,46]. The steps in those studies were taken as right/left according to whether it is gain/loss.…”

Section: Walk In the Gls: Comparison To A Lazy Walkermentioning

confidence: 99%

“…In some earlier works studying the dynamics of the transactions, a walk was conceived for the agents in an abstract one-dimensional gain–loss space (GLS) [45,46]. The corresponding walk was compared to a biased random walk.…”

Section: Introductionmentioning

confidence: 99%

A poor agent and subsidy: an investigation through CCM model

Goswami

2022

Phil. Trans. R. Soc. A.

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In this work, the dynamics of agents below a threshold line in some modified CCM type kinetic wealth exchange models are studied. These agents are eligible for subsidy as can be seen in any real economy. An interaction is prohibited if both of the interacting agents’ wealth fall below the threshold line. A walk for such agents can be conceived in the abstract gain–loss space (GLS) and is macroscopically compared to a lazy walk. The effect of giving subsidy once to such agents is checked over, giving repeated subsidy from the point of view of the walk in GLS. It is seen that the walk has more positive drift if the subsidy is given once. The correlations and other interesting quantities are studied. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.

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“…For financial data, a random walk picture was introduced initially by Louis Bachelier [18]. Later, similar walks were studied for models of wealth exchange [19,20].…”

Section: Introductionmentioning

confidence: 99%

Virtual walks inspired by a mean field kinetic exchange model of opinion dynamics

Saha,

Sen

2022

Preprint

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We propose two different schemes of realizing a virtual walk corresponding to a kinetic exchange model of opinion dynamics. The walks are either Markovian or non-Markovian in nature. The opinion dynamics model is characterized by a parameter p which drives an order disorder transition at a critical value pc. The distribution S(X, t) of the displacements X from the origin of the walkers is computed at different times. Below pc, two time scales associated with a crossover behavior in time are detected, which diverge in a power law manner at criticality with different exponent values. S(X, t) also carries the signature of the phase transition as it changes its form at pc. The walks show the features of a biased random walk below pc, and above pc, the walks are like unbiased random walks. The bias vanishes in a power law manner at pc and the width of the resulting Gaussian function shows a discontinuity. Some of the features of the walks are argued to be comparable to the critical quantities associated with the mean field Ising model, to which class the opinion dynamics model belongs. The results for the Markovian and non-Markovian walks are almost identical which is justified by considering the different fluxes. We compare the present results with some earlier similar studies.

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Antipersistent dynamics in kinetic models of wealth exchange

Cited by 5 publications

References 38 publications

Virtual walks in spin space: A study in a family of two-parameter models

Virtual walks in spin space: A study in a family of two-parameter models

A poor agent and subsidy: an investigation through CCM model

Virtual walks inspired by a mean field kinetic exchange model of opinion dynamics

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