The stable Ramsey’s theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are non-null in a certain effective measure-theoretic sense. We show that the sets that can compute infinite homogeneous sets for non-null many computable stable colorings and ...

The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent vertices in a graph such that no unpaired vertices prefer each other to their partners under the matching. The problem of finding stable matchings is known as the s...

It is shown that max-stable random vectors in [0,∞)d with unit Fréchet marginals are in one to one correspondence with convex sets K in [0,∞)d called max-zonoids. The max-zonoids can be characterised as sets obtained as limits of Minkowski sums of cross-polytopes or, alternatively, as the selection expectation of a random crosspolytope whose distribution is controlled by the spectral measure of...

We introduce a class of random compact metric spaces Lα indexed by α ∈ (1, 2) and which we call stable looptrees. They are made of a collection of random loops glued together along a tree structure, and can informally be viewed as dual graphs of α-stable Lévy trees. We study their properties and prove in particular that the Hausdorff dimension of Lα is almost surely equal to α. We also show tha...

Abstract Many tasks (e.g., clustering) in machine learning only require the lα distances instead of the original data. For dimension reductions in the lα norm (0 < α ≤ 2), the method of stable random projections can efficiently compute the lα distances in massive datasets (e.g., the Web or massive data streams) in one pass of the data. The estimation task for stable random projections has been ...

We investigate the perturbation of the non-linear differential equation dx(t) dt = f(x(t)) by random noise terms consisting of Brownian motion and an independent Poisson random measure. We find conditions under which the perturbed system is almost surely exponentially stable and estimate the corresponding Lyapunov exponents.

We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration results for some other functionals of these random matrices, such as the largest eigenvalue or the largest singular value. AMS 2000 Subject Classification: 60E07, 60F10, 15A42, 15A52

Let ( ) ( ) ( ) ( ) be a sequence of mutually independent, identically distributed random variables following semi-stable distribution with characteristic function ( ( ) ) . In this work, we obtain the lower bound of the number of real zeros of the random algebraic equation∑ ( ) . ( ) denote the number of real roots must ( ⁄ ) , except for a set of measure at most .

where m(f(X)) is a median of f(X) and where Φ is the (one–dimensional) standard normal distribution function. The inequality (1) has seen many extensions and to date, most of the conditions under which these developments hold require the existence of finite exponential moments for the underlying vector X . It is thus natural to explore the robustness of this “concentration phenomenon” and to st...