We develop a scale-invariant truncated Lévy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits Lévy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the advantage...

We present numerical simulations of two-dimensional models of electric breakdown and fracture in disordered systems subject to an increasing external stress. We provide a geometrical characterization of the damage by studying the scaling behavior of connected bonds clusters. The average cluster...

Financial markets exhibit a complex hierarchy among different processes, e.g. a trading time marks the initiation of a trade, and a trade triggers a price change. High-frequency trading data arrive at random times. By combining stochastic and agent-based approaches, we develop a model for...

A thermodynamical formalism for resistor networks is developed in order to extract full information on the multifractal scaling structure. We introduce a matrix representation and study the moments of the voltage distribution Z̃(β) = ∑i=1N|Vi|β α N -F̄(β) where N is the number of...

We model the time series of the S&P500 index by a combined process, the AR+GARCH process, where AR denotes the autoregressive process which we use to account for the short-range correlations in the index changes and GARCH denotes the generalized autoregressive conditional heteroskedastic process...

This manuscript is based on four opening lectures, which were designed to offer a brief and somewhat parochial overview of some “exotic” statistical physics puzzles of possible interest to biophysicists, medical physicists, and econophysicists. These include the statistical properties of DNA...

We discuss some apparently “universal” aspects observed in the empirical analysis of stock price dynamics in financial markets. Specifically we consider (i) the empirical behavior of the return probability density function and (ii) the content of economic information in financial time series.

We present exact results on the low-temperature behavior of the square lattice ±J Ising model, with a concentration c of ferromagnetic bonds and a concentration 1−c of antiferromagnetic bonds. We find that for T below a characteristic temperature T0, the system is “frozen” in the sense...

This talk will summarize the present status of an ongoing research program designed to answer the question posed in the title. Since a snapshot of liquid water with a subpicosecond shutter speed reveals that this system (a hydrogen-bonded liquid) is above its percolation threshold, it is...

We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children...