Abstract We present several Itô-Wentzell formulae on Wiener spaces for real-valued functional random field of Itô type that depend measure flows. distinguish the full- and marginal-measure flow cases in spirit mean-field games. Derivatives with respect to components are understood sense Lions.

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to e−|t| p and symmetric p-stable random variables, where p ∈ (0, 2]. We obtain various sharp moment an...

Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the “principle of conditioning”, to study their stable convergence towards mixtures of infinitely divisible distributions. Our results apply, in particular, to multiple integrals with respect to independently scattered and square ...

We initiate the study of weak containment and weak equivalence for μ-stationary actions for a given countable group G endowed with a generating probability measure μ. We show that Furstenberg entropy is a stable weak equivalence invariant, and furthermore is a continuous affine map on the space of stable weak equivalence classes. We prove the same for the associated stationary random subgroup (...

We reformulate various versions of infinitely divisible cascades proposed in the literature using stochastic equations. This approach sheds a new light on the differences and common points of several formulations that have been recently provided by several teams. In particular, we focus on the simplification occurring when the infinitely divisible noise at the heart of such model is stable: an ...

We generalize a recent result of Haagerup; namely we show that a convolution with a standard Gaussian random matrix regularizes the behavior of Fuglede–Kadison determinant and Brown spectral distribution measure. In this way it is possible to establish a connection between limit eigenvalues distributions of a wide class of random matrices and the Brown measure of the corresponding limits.

Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it wit...

We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure μ̂ of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N ×N symmetric matrix YσN whose (i, j) entry is σ( i N , j N )xij where (xij , 1 ≤ i ≤ j < ∞) is an infinite array of i.i.d real variables with common distribution in the domain of attraction of an α-...

A recent study examined the stability of rankings from random forests using two variable importance measures (mean decrease accuracy (MDA) and mean decrease Gini (MDG)) and concluded that rankings based on the MDG were more robust than MDA. However, studies examining data-specific characteristics on ranking stability have been few. Rankings based on the MDG measure showed sensitivity to within-...