arXiv subjects

Roy Wagner

Publications and source records attributed to Roy Wagner.

3 recordsLinked to original sources

arXiv2007

Tail estimates for sums of variables sampled from a random walk

We prove tail estimates for variables $\sum_i f(X_i)$, where $(X_i)_i$ is the trajectory of a random walk on an undirected graph (or, equivalently, a reversible Markov chain). The estimates are in terms of the maximum of the function $f$, its variance, and the spectrum of the graph. Our proofs are more elementary than other proofs in the literature, and our results are sharper. We obtain Bernstein and Bennett-type inequalities, as well as an inequality for subgaussian variables.

math.PR↗

arXiv2005

On the extremality of Hofer's metric on the group of Hamiltonian diffeomorphisms

Let M be a closed symplectic manifold, and let | | be a norm on the space of all smooth functions on M, which are zero-mean normalized with respect to the canonical volume form. We show that if | | is dominated from above by the L-Infinity-norm, and | | is invariant under the action of Hamiltonian diffeomorphisms, then it is also invariant under all volume preserving diffeomorphisms. We also prove that if | | is, additionally, not equivalent to the L-Infinity-norm, then the induced Finsler metric on the group of Hamiltonian diffeomorphisms on M vanishes identically.

math.SG↗

arXiv1997

Proximity to $\ell_1$ and Distortion in Asymptotic $\ell_1$ Spaces

For an asymptotic $\ell_1$ space $X$ with a basis $(x_i)$ certain asymptotic $\ell_1$ constants, $δ_α(X)$ are defined for $α<ω_1$. $δ_α(X)$ measures the equivalence between all normalized block bases $(y_i)_{i=1}^k$ of $(x_i)$ which are $S_α$-admissible with respect to $(x_i)$ ($S_α$ is the $α^{th}$-Schreier class of sets) and the unit vector basis of $\ell_1^k$. This leads to the concept of the delta spectrum of $X$, $Δ(X)$, which reflects the behavior of stabilized limits of $δ_α(X)$. The analogues of these constants under all renormings of $X$ are also defined and studied. We investigate $Δ(X)$ both in general and for spaces of bounded distortion. We also prove several results on distorting the classical Tsirelson's space $T$ and its relatives.

math.FA↗