We propose a recursive method for the computation of cumulants self-exciting point processes Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement higher-order in comparison with existing methods differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and al...

We present direct statistical simulation of jet formation on a β plane, solving for the statistics of a fluid flow via an expansion in cumulants. Here we compare an expansion truncated at second order (CE2) to statistics accumulated by direct numerical simulations. We show that, for jets near equilibrium, CE2 is capable of reproducing the jet structure (although some differences remain in the s...

Factorial moments and cumulants are usually defined with respect to the unconditioned Poisson process. Conditioning a sample by selecting events of a given overall multiplicity N necessarily introduces correlations. By means of Edgeworth expansions, we derive generalized cumulants which define correlations with respect to an arbitrary process rather than just the Poisson case. The results are a...

We report on an analytical study of the statistics of conductance, g, and shot-noise power, p, for a chaotic cavity with arbitrary numbers N1,2 of channels in two leads and symmetry parameter β = 1, 2, 4. With the theory of Selberg’s integral the first four cumulants of g and first two cumulants of p are calculated explicitly. We give analytical expressions for the conductance and shot-noise di...

We have calculated the large-q series of the energy cumulants, the magnetization cumulants and the correlation length at the first order phase transition point both in the ordered and disordered phases for the q-state Potts model in two dimensions. The series enables us to estimate the numerical values of the quantities more precisely by a factor of 102−104 than the Monte Carlo simulations. Fro...

Within the framework of random multiplicative energy cascade models of fully developed turbulence, finite-size-scaling expressions for two-point correlators and cumulants are derived, taking into account the observationally unavoidable conversion from an ultrametric to an Euclidean two-point distance. The comparison with two-point statistics of the surrogate energy dissipation, extracted from v...

We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have nonnegative integer coefficients. This extends recent results about normalized characters of the symmetric group. 2000 Mathematics Subject Classification: 05...