Publications by authors named "Erez Aghion"
Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.
View Article and Find Full Text PDFVarious mathematical Black-Scholes-Merton-like models of option pricing employ the paradigmatic stochastic process of geometric Brownian motion (GBM). The innate property of such models and of real stock-market prices is the roughly exponential growth of prices with time [on average, in crisis-free times]. We here explore the ensemble- and time averages of a multiplicative-noise stochastic process with power-law-like time-dependent volatility, σ(t)∼t^{α}, named scaled GBM (SGBM).
View Article and Find Full Text PDFFrom Non-Normalizable Boltzmann-Gibbs Statistics to Infinite-Ergodic Theory.
Phys Rev Lett
January 2019
We study a particle immersed in a heat bath, in the presence of an external force which decays at least as rapidly as 1/x, e.g., a particle interacting with a surface through a Lennard-Jones or a logarithmic potential.
View Article and Find Full Text PDFArticle Synopsis
- This study introduces a new method to analyze large fluctuations in systems with heavy-tailed distributions, where traditional large-deviations theory isn’t applicable.
- It focuses on the spatial density of laser-cooled atoms, particularly looking at rare events that significantly impact the system's statistical properties.
- The research employs a unique friction mechanism from laser fields and unveils a bifractal nature in the spreading process, providing new relationships that broaden the theory to systems with multifractal characteristics.
Article Synopsis
- An exact solution for the distance distribution between monomers in ring polymers is presented, showing that for both non-interacting and local-interaction models, the distributions relate closely to the area of Bessel bridges and excursions, especially in dimensions d ≥ 2.
- The study highlights a symmetry in dimensions, noting that dimension d and 4 - d are equivalent, meaning that Brownian excursion properties in 1D also apply to 3D ring polymers.
- Numerical results suggest that for self-avoiding polymers, average distance fluctuations are similar in dimensions 2 and 3, aligning with the non-interacting model's predictions in dimension 5.