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Journals and Conferences
We propose new methodologies in robust optimization that promise greater tractability, both theoretically and practically than the classical robust framework. We cover a broad range of mathematical optimization problems, including linear optimization (LP), quadratic constrained quadratic optimization (QCQP), general conic optimization including second order… (More)
For piecewise monotone interval maps we show that Kolmogorov-Sinai entropy can be obtained from order statistics of the values in a generic orbit. A similar statement holds for topological entropy.
We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the… (More)
We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given.
We prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on Z d. We assume that the transition probabilities of the walk depend not too strongly on the environment and that the evolution of the environment is Markovian with strong spatial and temporal mixing properties. 1. Introduction. The study… (More)
We present unpublished work of D. Carter, G. Keller, and E. Paige on bounded generation in special linear groups. Let n be a positive integer, and let A = O be the ring of integers of an algebraic number field K (or, more generally, let A be a localization OS). If n = 2, assume that A has infinitely many units. We show there is a finite-index subgroup H of… (More)
We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since neither the local maps need to have full branches nor the coupling map needs to be a homeomorphism of the infinite dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the… (More)
In this note we give a computable criterion for a piecewise expanding interval map T to be mixing, which at the same time not only establishes explicit bounds on the spectral gap of the associated Perron Frobenius operator acting on the space of functions of bounded variation, but establishes strict contraction rates for this operator. Of course such a… (More)