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Collective leadership and herding may arise in standard models of opinion dynamics as an interplay of a strong separation of time scales within the population and its hierarchical organization. Using the voter model as a simple opinion…
An interesting analog circuit for simulating a signal with fluctuations having a probability density function with a power tail has recently been proposed and constructed. The exponent of the power law can be fixed by tuning an appropriate…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
We extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model…
Starting from recent experimental observations of starlings and jackdaws, we propose a minimal agent-based mathematical model for bird flocks based on a system of second-order delayed stochastic differential equations with discontinuous…
We calculate the distribution of current fluctuations in two simple exclusion models. Although these models are classical, we recover even for small systems such as a simple or a double barrier, the same distibution of current as given by…
We consider the learning dynamics of a single reinforcement learning optimal execution trading agent when it interacts with an event driven agent-based financial market model. Trading takes place asynchronously through a matching engine in…
Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the "noise". Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted…
A three-state model based on the Potts model is proposed to simulate financial markets. The three states are assigned to "buy", "sell" and "inactive" states. The model shows the main stylized facts observed in the financial market:…
We present a spectral-theoretic approach to time-average statistical mechanics for general, non-equilibrium initial conditions. We consider the statistics of bounded, local additive functionals of reversible as well as irreversible ergodic…
This thesis is dedictaed to the study of fluctuation and correlation observables of hadronic equilibrium systems. The statistical hadronization model of high energy physics, in its ideal, i.e. non-interacting, gas approximation will be…
We discuss the stationary states of a model economy in which $N$ heterogeneous adaptive consumers purchase commodity bundles repeatedly from $P$ sellers. The system undergoes a transition from an inefficient to an efficient state as the…
In this work, we propose an order book model with herd behavior. The proposed model is built upon two distinct approaches: a recent empirical study of the detailed order book records by Kanazawa et al. [Phys. Rev. Lett. 120, 138301] and…
We consider the collective behaviour of active particles that locally align with their neighbours. Agent-based simulation models have previously shown that in one dimension, these particles can form into a flock that maintains its stability…
The existence of a (partial) market equilibrium price is proved in a complete, continuous time finite-agent market setting. The economic agents act as price takers in a fully competitive setting and maximize exponential utility from…
In this paper, we reconsider the spin model suggested recently to understand some features of collective decision making among higher organisms [A.T. Hartnett et al., Phys. Rev. Lett. 116 (2016) 038701]. Within the model, the state of an…
We introduce and solve a model of fermions hopping between neighbouring sites on a line with random Brownian amplitudes and open boundary conditions driving the system out of equilibrium. The average dynamics reduces to that of the…
Living systems often function with regulatory interactions, but the question of how activity, stochasticity and regulations work together for achieving different goals still remains puzzling. We propose a stochastic model of an active…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
The structure of very complicated irregular "microscopic" (local) entropy fluctuations around a big separated "macroscopic" (global) fluctuation in the statistical equilibrium was studied in numerical experiments on a simple 2--freedom…