22 citations · 52 across the 14 of their papers we have counts for
9 papers · 1 filter
What can be the limit in the CLT for a field of martingale differences?
Davide Giraudo, Emmanuel Lesigne, Dalibor Volny
The now classical convergence in distribution theorem for well normalized sums ofstationary martingale increments has been extended to multi-indexed martingaleincrements (see Volný…
Random Sequences and Pointwise Convergence of Multiple Ergodic Averages
Nikos Frantzikinakis, Emmanuel Lesigne, Mate Wierdl
We prove pointwise convergence, as , for the multiple ergodic averages , where and are commuting measure pres…
Averages on annuli of Eulidean space
Emmanuel Lesigne, François Havard
We study the range of validity of differentiation theorems and ergodic theorems for actions, for averages on "thick spheres" of Euclidean space.
Powers of sequences and convergence of ergodic averages
Nikos Frantzikinakis, Michael Johnson, Emmanuel Lesigne +1
A sequence of integers is good for the mean ergodic theorem if for each invertible measure preserving system and any bounded measurable function ,…
Powers of sequences and recurrence
Nikos Frantzikinakis, Emmanuel Lesigne, Mate Wierdl
We study recurrence, and multiple recurrence, properties along the -th powers of a given set of integers. We show that the property of recurrence for some given values of do…
Intersective polynomials and polynomial Szemeredi theorem
Vitaly Bergelson, Alexander Leibman, Emmanuel Lesigne
Let $P=\{p_{1},\ld,p_{r}\}\subset\Q[n_{1},\ld,n_{m}]$ be a family of polynomials such that $p_{i}(\Z^{m})\sle\Z$, $i=1,\ld,r$. We say that the family has {\it PSZ property} if…
Van der Corput sets in Z^d
Vitaly Bergelson, Emmanuel Lesigne
In this partly expository paper we study van der Corput sets in , with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical…
Mild mixing property for special flows under piecewise constant functions
K. Fraczek, M. Lemanczyk, E. Lesigne
We give a condition on a piecewise constant roof function and an irrational rotation by on the circle to give rise to a special flow having the mild mixing property. Such flows…
Sets of k-recurrence but not (k+1)-recurrence
N. Frantzikinakis, E. Lesigne, M. Wierdl
For every , we produce a set of integers which is -recurrent but not -recurrent. This extends a result of Furstenberg who produced a 1-recurrent set whic…