We derive exact expressions for the excess number of clusters b and the excess cumulants b n of a related quantity at the 2-D percolation point. High-accuracy computer simulations are in accord with our predictions. b is a finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula for the number of clusters per site n c in the infinite system limit; the b n correct bulk cum...

We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixt...

Kerov’s polynomials give irreducible character values of the symmetric group in term of the free cumulants of the associated Young diagram. Using a combinatorial approach with maps, we prove in this article a positivity result on their coefficients, which extends a conjecture of S. Kerov. Résumé. Les polynômes de Kerov expriment les valeurs des caractères irréductibles du groupe symmétrique en ...

In this paper, we address the problem of estimating the parameters of a noncausal autoregressive (AR) signal from estimates of the higher-order cumulants of noisy observations. The proposed family of techniques uses both 3rd-order and 4thorder cumulants of the observed output data. Consequently, at low SNR, they provide superior performance to methods based on autocorrelations. The measurement ...

We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on identifying the current cumulants from a Rayleigh-Schrödinger perturbation expansion for the generating function. Here it is derived from a simple path-distributi...

The fractal nature of Internet traffic has been observed by several measurements and statistical studies. In this paper a new monofractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differential Generator (LISDLG) is presented, which effectively characterizes network traffic monofractality. Several properties of the LISDLG model are present...

Estimation of third-order statistics relies on the availability a huge amount data records, which can pose severe challenges collecting hardware in terms considerable storage costs, overwhelming energy consumption, and unaffordably high sampling rate especially when dealing with high-dimensional such as wideband signals. To overcome these challenges, this paper focuses reconstruction cumulants ...