Related papers: Derivation of the universal decay cascade distribu…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
We produce uniform and decaying bounds in time for derivatives of the solution to the backwards Kolmogorov equation associated to a stochastic processes governed by a time dependent dynamics. These hold under assumptions over the…
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…
This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…
It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these…
We determine the probability distribution of the breaking strength for chains of N links, which have been produced by repeatedly breaking a very long chain.
For the steady-state direct cascade of two-dimensional Navier-Stokes turbulence, we derive analytically the probability of strong vorticity fluctuations. The probability density function (pdf) of the vorticity coarse-grained over a scale in…
We define and study a family of distributions with domain complete Riemannian manifold. They are obtained by projection onto a fixed tangent space via the inverse exponential map. This construction is a popular choice in the literature for…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
High resolution direct numerical simulations of two-dimensional turbulence in stationary conditions are presented. The development of an energy-enstrophy double cascade is studied and found to be compatible with the classical Kraichnan…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.
Selected examples of possible origins of power-law distributions are presented.
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
We generalise the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the (2 -> 2) scattering of all the pseudoscalar octet mesons (pi, K, eta). We formulate it in a general way and include…
For basic discrete probability distributions, $-$ Bernoulli, Pascal, Poisson, hypergeometric, contagious, and uniform, $-$ $q$-analogs are proposed.
In this article we prove results concerning upper and lower decay estimates for homogeneous Sobolev norms of solutions to a rather general family of parabolic equations. Following the ideas of Kreiss, Hagstrom, Lorenz and Zingano, we use…
In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to sums of…