We study the convergence of the population dynamics algorithm, which produces sample pools of random variables having a distribution that closely approximates that of the special endogenous solution to a stochastic fixed-point equation of the form: R D = Φ(Q,N, {Ci}, {Ri}), where (Q,N, {Ci}) is a real-valued random vector with N ∈ N, and {Ri}i∈N is a sequence of i.i.d. copies of R, independent ...

We introduce a novel method for analyzing a well known class of adaptive algorithms. By combining recent developments from the theory of Markov processes and long existing results from t h e theory of Perturbations of Linear Operators we s tudy first the behavior and convergence properties of a class of products of random matrices. This i n t u r n allows for the analysis of t h e first a n d s...

Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and a translation conditional on the spin state. Coined quantum walks on Z can be treated as special cases of coined quantum walks on R. We study quantum walks ...

We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational approximation by taking the minimum over the regular grid, which consists of rational points with denominator r (for given r). We show that the associated convergen...

We study approximative identities In(f)(x) = 1 2 Z ? n(u)f(x ? u) du with positive even trigonometric polynomials n of degree n as kernels. It is well known that in general the approximants In(f) are norm convergent to f with order at most n ?2 and that convergence for the test function f(x) = (2 sin(x=2)) 2 at x = 0 implies norm convergence for a wide class of functions f. We discuss the order...