Michel Weber
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Michel Weber has a total of 8 co-authors. Here are the top co-authors by number of shared publications:
- Mikhail Lifshits
St.Petersburg State University, St.Petersburg, Russia
4 shared publications - István Berkes
Institute of Statistics Graz University of Technology Kopernikusgasse 24 8010 Graz Austria
3 shared publications - Mikhail Lifshits
St-Petersburg, 197372, Komendantskii, 22-2-49, Russia
2 shared publications - Fakhr Eddine Boukhari1 shared publication
- Michael Lin
Department of Mathematics, Ben-Gurion University of The Negev, Beer-Sheva, Israel
1 shared publication Rita Giuliano Antonini
1 shared publication
Latest Publications
- 10 August 2011
- Published by Taylor & Francis in Stochastic Analysis and Applications
- Vol. 29 (5) , 779-798
Almost Sure Local Limit Theorems with Rate
We establish almost sure versions, with rate, of the local limit theorem for lattice distributed random variables. We also prove a new delicate correlation inequality for sums of i.i.d. lattice distributed random variables.
- 10 August 2011
- Published by Taylor & Francis in Stochastic Analysis and Applications
- Vol. 29 (5) , 779-798
Almost Sure Local Limit Theorems with Rate
We establish almost sure versions, with rate, of the local limit theorem for lattice distributed random variables. We also prove a new delicate correlation inequality for sums of i.i.d. lattice distributed random variables.
- Open Access
Dirichlet polynomials: some old and recent results, and their interplay in number theory
In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and continue with some investigations concerning their supremum properties. Their random counterpart is considered in the last part of the paper, where a analysis of their supremum properties, based on methods of stochastic processes, is developed.
Open AccessDirichlet polynomials: some old and recent results, and their interplay in number theory
In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and continue with some investigations concerning their supremum properties. Their random counterpart is considered in the last part of the paper, where a analysis of their supremum properties, based on methods of stochastic processes, is developed.
- Open Access
A Sharp Estimate for Divisors of Bernoulli Sums
Let $S_n=\e_1+...+\e_n$, where $ \e_i $ are i.i.d. Bernoulli r.v.'s. Let $0\le r_d(n)<2d$ be the least residue of $n$ mod$(2d)$, $\bar r_d(n)= 2d -r_d(n)$ and $\b(n,d)=\max ({1\over d}, {1\over \sqrt n})[e^{- {r_d(n)^2/2 n}} +e^{- {\bar r_d(n)^2/2 n}}]$. We show that $$\sup_{2\le d\le n} \big|\P\big\{d|S_n\big\}- E(n,d) \big|= {\cal O}\big({\log^{5/2} n \over n^{3/2}}\big), $$ where $E(n,d) $ verifies $c_1\b(n,d)\le E(n,d)\le c_2\b(n,d) $ and $c_1,c_2 $ are numerical constants.Open AccessA Sharp Estimate for Divisors of Bernoulli Sums
Let $S_n=\e_1+...+\e_n$, where $ \e_i $ are i.i.d. Bernoulli r.v.'s. Let $0\le r_d(n)<2d$ be the least residue of $n$ mod$(2d)$, $\bar r_d(n)= 2d -r_d(n)$ and $\b(n,d)=\max ({1\over d}, {1\over \sqrt n})[e^{- {r_d(n)^2/2 n}} +e^{- {\bar r_d(n)^2/2 n}}]$. We show that $$\sup_{2\le d\le n} \big|\P\big\{d|S_n\big\}- E(n,d) \big|= {\cal O}\big({\log^{5/2} n \over n^{3/2}}\big), $$ where $E(n,d) $ verifies $c_1\b(n,d)\le E(n,d)\le c_2\b(n,d) $ and $c_1,c_2 $ are numerical constants. - Open Access
A general strong law of large numbers for additive arithmetic functions
Let $f(n)$ be a strongly additive complex valued arithmetic function. Under mild conditions on $f$, we prove the following weighted strong law of large numbers: if $ X,X_1,X_2,... $ is any sequence of integrable i.i.d. random variables, then $$ \lim_{N\to \infty} {\sum_{n=1}^N f(n) X_n \over\sum_{n=1}^N f(n)} \buildrel{a.s.}\over{=} \E X . $$Open AccessA general strong law of large numbers for additive arithmetic functions
Let $f(n)$ be a strongly additive complex valued arithmetic function. Under mild conditions on $f$, we prove the following weighted strong law of large numbers: if $ X,X_1,X_2,... $ is any sequence of integrable i.i.d. random variables, then $$ \lim_{N\to \infty} {\sum_{n=1}^N f(n) X_n \over\sum_{n=1}^N f(n)} \buildrel{a.s.}\over{=} \E X . $$ - Open Access
On Mean Values of Dirichlet Polynomials
We show a general lower bound for Mean-value of Dirichlet polynomials
Open AccessOn Mean Values of Dirichlet Polynomials
We show a general lower bound for Mean-value of Dirichlet polynomials
- Open Access
A Remark on Zeros of Brownian Motion
Let $ \{W(t), t\ge 0\}$ be a standard Brownian motion. If $I$ is a bounded interval on which $W $ has no zero, an almost sure lower bound to $\inf\{|W(t)|, t\in I\}$ can be provided, when $I$ is taken from a given countable family of intervals covering the positive half-line.Open AccessA Remark on Zeros of Brownian Motion
Let $ \{W(t), t\ge 0\}$ be a standard Brownian motion. If $I$ is a bounded interval on which $W $ has no zero, an almost sure lower bound to $\inf\{|W(t)|, t\in I\}$ can be provided, when $I$ is taken from a given countable family of intervals covering the positive half-line. - Open Access
On the Supremum of Some Random Dirichlet Polynomials
We study the supremum of some random Dirichlet polynomials with independent coefficients and obtain sharp upper and lower bounds for supremum expectation thus extending the results from our previous work (see http://arXiv.org/abs/math/0703691). Our approach in proving these results is entirely based on methods of stochastic processes, in particular the metric entropy method.
Open AccessOn the Supremum of Some Random Dirichlet Polynomials
We study the supremum of some random Dirichlet polynomials with independent coefficients and obtain sharp upper and lower bounds for supremum expectation thus extending the results from our previous work (see http://arXiv.org/abs/math/0703691). Our approach in proving these results is entirely based on methods of stochastic processes, in particular the metric entropy method.
- Open Access
Supremum of Random Dirichlet Polynomials with Sub-multiplicative Coefficients
We study the supremum of random Dirichlet polynomials $D_N(t)=\sum_{n=1}^N\varepsilon_n d(n) n^{- s}$, where $(\varepsilon_n)$ is a sequence of independent Rademacher random variables, and $ d $ is a sub-multiplicative function. The approach is gaussian and entirely based on comparison properties of Gaussian processes, with no use of the metric entropy method.Open AccessSupremum of Random Dirichlet Polynomials with Sub-multiplicative Coefficients
We study the supremum of random Dirichlet polynomials $D_N(t)=\sum_{n=1}^N\varepsilon_n d(n) n^{- s}$, where $(\varepsilon_n)$ is a sequence of independent Rademacher random variables, and $ d $ is a sub-multiplicative function. The approach is gaussian and entirely based on comparison properties of Gaussian processes, with no use of the metric entropy method. - 28 March 2009
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 23 (2) , 428-446
Upper-Lower Class Tests for Weighted i.i.d. Sequences and Martingales
- 28 March 2009
- Published by Springer Nature in Journal of Theoretical Probability
- Vol. 23 (2) , 428-446
Upper-Lower Class Tests for Weighted i.i.d. Sequences and Martingales
- 19 January 2009
- Published by Springer Nature in Results in Mathematics
- Vol. 53 (1-2) , 197-200
Divisors of Bernoulli Sums
- 19 January 2009
- Published by Springer Nature in Results in Mathematics
- Vol. 53 (1-2) , 197-200
Divisors of Bernoulli Sums