1 citations · 2 across the 8 of their papers we have counts for
14 papers
Dudley-type bound for stationary Bernoulli processes
W. Bednorz, R. Martynek, R. Meller
This is preliminary, AI-generated note on the Dudley-type bound for stationary Bernoulli processes postulated by M. Talagrand based on the unpublished notes of the authors and the…
Sudakov Minoration for Unconditional Log-Concave Vectors
Witold Bednorz, Rafal Martynek, Rafal Meller
Sudakov minoration asks whether a large family of separated random linear forms must have a large expected maximum. We present a proof candidate for this principle for all uncondit…
Sudakov minoration for unconditional log-concave vectors with negatively associated magnitudes
Witold Bednorz, Rafal Martynek, Rafal Meller
We prove the Sudakov minoration principle, with a universal constant, for unconditional log-concave random vectors whose coordinate magnitudes are negatively associated. The main s…
Operator-norm Sudakov minoration for Gaussian chaos of order two
Witold Bednorz, Rafał Martynek, Rafał Meller
We prove that an operator-norm separated family of matrices satisfies , where G,G' are independent standard Gaussian vectors and a…
A Gaussian Chain Rule Proof of the Banach Space Hanson Wright Bound
Witold Bednorz, Rafal Martynek, Rafal Meller
For a finite family of real matrices, we bound the Gaussian width of the union of its image ellipsoids by its maximal Hilbert Schmidt norm, its maximal fixed input Gaussian width,…
A candidate proof of the sharp Latala and Strzelecka Gaussian matrix bound
Witold Bednorz, Rafal Martynek, Rafal Meller
We give a candidate proof of Conjecture 5 in the third arXiv version of Latala and Strzelecka Operator lp lq norms of Gaussian matrices.
An invariant variational proof for canonical processes with independent symmetric log-concave tails
Witold Bednorz, Rafal Martynek, Rafal Meller
We prove a prescribed-index-law comparison for canonical processes with independent symmetric coordinates having log-concave tails, with no doubling assumption
Small cover approach to the suprema of positive canonical processes
Witold Bednorz, Rafał Martynek, Rafał Meller
We extend the recent result of Park and Pham concerning the positive selector process to canonical processes generated by i.i.d. nonnegative random variables satisfying minimal tai…
The suprema of selector processes with the application to positive infinitely divisible processes
Witold Bednorz, Rafał Martynek, Rafał Meller
We provide an alternative proof of the recent result by Park and Pham (2022) on the expected suprema of positive selector and empirical processes. We extend it to positive infinite…
The suprema of infinitely divisible processes
Witold Bednorz, Rafał Martynek
In this paper we complete the full characterization of the expected suprema of infinitely divisible processes. In particular, we remove the technical assumption called …
A Lévy-Ottaviani type inequality for the Bernoulli process on an interval
Witold Bednorz, Rafał Martynek
In this paper we prove a Lévy-Ottaviani type of property for the Bernoulli process defined on an interval. Namely, we show that under certain conditions on functions $(a_i)_{i=1}^{…
On a contraction property of Bernoulli canonical processes
Witold Bednorz, Rafał Martynek
In this paper we improve Bernoulli comparison. The result works for independent Rademacher random variables and states that we can compare $\mathbb{E}\su…
Optimal uniform approximation of Lévy processes on Banach spaces with finite variation processes
W. M. Bednorz, Rafał M. Łochowski, R. Martynek
For a general càdlàg Lévy process on a separable Banach space we estimate values of $\inf_{Y\in{\cal A}_X} \mathbb{E}\left\{ ψ\left( \Vert X - Y \Vert_\infty\right) + \mathrm{T…
On tails of symmetric and totally asymmetric -stable distributions
Witold M. Bednorz, Rafał M. Łochowski, Rafał Martynek
We estimate up to universal constants tails of symmetric and totally asymmetric 1-dimensional -stable distributions in terms of functions of the parameters of these distribution…