On an identity of Ky Fan
We give several applications of an identity for sums of weakly stationary sequences due to Ky Fan.
math.DS↗
arXiv subjects
Michel Weber
Publications and source records attributed to Michel Weber.
Divisors of Bernoulli sums
We study the asymptotic behavior of the sums of divisors when the integers are modelled with the Bernoulli random walk; We prealably study the correlation properties of the corresponding system.
math.PR↗
Sampling the Lindelöf Hypothesis with the Cauchy Random Walk
We study the behavior of the Riemann zeta function on the critical line when the imaginary part of the argument is sampled by the Cauchy random walk. We develop a complete second order theory for the corresponding system of random variables and show that it behaves almost like a system of non-correlated variables. Exploiting this fact in relation with known criteria for almost sure convergence allows to investigate its almost sure asymptotic behavior.
math.PR↗
On the Supremum of Random Dirichlet Polynomials
We study the supremum of some random Dirichlet polynomials and obtain sharp upper and lower bounds for supremum expectation that extend the optimal estimate of Halász-Queffélec and enable to cunstruct random polynomials with unusually small maxima. Our approach in proving these results is entirely based on methods of stochastic processes, in particular the metric entropy method.
math.PR↗