We apply an asymmetric version of Kirman’s herding model to volatile financial markets. In the relation between returns and agent concentration we use the square root law proposed by Zhang. This can be derived by extending the idea of a critical mean field theory suggested by Plerou et al. We show that this model is equivalent to the so called 3/2-model of stochastic volatility. The description...

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as the area distribution in the model of self-avoiding loops.

We provide a large deviation result for a random sum ∑ Nx n=0 Xn, where Nx is a renewal counting process and {Xn}n≥0 are i.i.d. random variables, independent of Nx, with a common distribution that belongs to a class of square root insensitive distributions. Asymptotically, the tails of these distributions are heavier than e− √ x and have zero relative decrease in intervals of length √ x, hence ...

Square root laws state that the capacity of an imperfect stegosystem – where the embedding does not preserve the cover distribution exactly – grows with the square root of cover size. Such laws have been demonstrated empirically and proved mathematically for a variety of situations, but not for nonstationary covers. Our aim here is to examine a highly simplified nonstationary source, which can ...

The estimation of average-power dissipation of a circuit through exhaustive simulation is impractical due to the large number of primary inputs and their combinations. In this brief, two algorithms based on least square estimation are proposed for determining the average power dissipation in complementary metal–oxide–semiconductor (CMOS) circuits. Least square estimation converges faster by att...

We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial di...

We apply the holonomic gradient method to compute the distribution function of a weighted sum of independent noncentral chi-square random variables. It is the distribution function of the squared length of a multivariate normal random vector. We treat this distribution as an integral of the normalizing constant of the Fisher-Bingham distribution on the unit sphere and make use of the partial di...

In this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic Ising system consisting of magnetic atoms with spin-1. This study is done using the effectivefield theory (EFT) with correlations method. The equations are derived using...