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A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

Publications associées (35)

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For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Dimensionality Reduction in Dynamic Optimization under Uncertainty

Napat Rujeerapaiboon

Dynamic optimization problems affected by uncertainty are ubiquitous in many application domains. Decision makers typically model the uncertainty through random variables governed by a probability distribution. If the distribution is precisely known, then ...

EPFL2016

The Chaining Lemma and Its Application

Sebastian Faust

We present a new information-theoretic result which we call the Chaining Lemma. It considers a so-called "chain" of random variables, defined by a source distribution X-(0) with high min-entropy and a number (say, t in total) of arbitrary functions (T-1,.. ...

Springer-Verlag Berlin2015

Adaptive polynomial approximation by means of random discrete least squares

Giovanni Migliorati

We address adaptive multivariate polynomial approximation by means of the discrete least-squares method with random evaluations, to approximate in the L2 probability sense a smooth function depending on a random variable distributed according to a given pr ...

Springer2015

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

Algebraic Trace Functions Over The Primes

Philippe Michel

We study sums over primes of trace functions of l-adic sheaves. Using an extension of our earlier results on algebraic twists of modular forms to the case of Eisenstein series and bounds for Type II sums based on similar applications of the Riemann hypothe ...

Duke Univ Press2014

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this paper, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a para ...

MATHICSE2014

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Erik Gustaf Bogislaw Von Schwerin, Hakon Andreas Hoel

We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both b ...

Siam Publications2014

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

MATHICSE2013

Some applications of the Weil-Barner explicit formula

Thorsten Kleinjung

The Weil-Barner explicit formula is applied to the prime counting function and to the problem of numerical partial verification of the Riemann hypothesis. ...

Wiley-V C H Verlag Gmbh2013