10 citations · 21 across the 12 of their papers we have counts for
19 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AI-generated note on the Dudley-type bound for stationary Bernoulli processes postulated by M. Talagrand based on the unpublished notes of the authors and the…
Moment estimates for chaoses with regular moment growth
Rafał Meller
We give two-sided moment estimates for decoupled chaoses of any order generated by independent symmetric random variables with regular moment growth: for e…
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.
A short proof of the Bernoulli decomposition theorem
Witold Bednorz Rafal Martynek, Rafal Meller
We give a construction of admissible partitions that yields the Bernoulli decomposition theorem
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
Sudakov minoration for weighted Orlicz balls
Witold Bednorz, Witold Bednorz Rafal Martynek, Rafal Meller +1
We give a proof of a universal Sudakov minoration principle for measures based on wighted Orlicz balls.
Spectral norm of matrices with independent entries up to polyloglog
Rafał Meller
In this paper, we study the expectation of the operator norm of the random matrix (a_{ij} X_{ij}) for i,j <= n, under the assumption that the random variables (X_{ij}) are independ…
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…
Moments and tails of Lq-valued chaoses based on independent variables with log-concave tails
Rafał Meller
We derive a lower bound for moments of random chaoses of order two with coefficients in arbitrary Banach space F generated by independent symmetric random variables with logarithmi…
Moments of Gaussian chaoses in Banach spaces
Radosław Adamczak, Rafał Latała, Rafał Meller
We derive moment and tail estimates for Gaussian chaoses of arbitrary order with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it h…
Hanson-Wright inequality in Banach spaces
Radosław Adamczak, Rafał Latała, Rafał Meller
We discuss two-sided bounds for moments and tails of quadratic forms in Gaussian random variables with values in Banach spaces. We state a natural conjecture and show that it holds…
Tail and moment estimates for a class of random chaoses of order two
Rafał Meller
We derive two-sided bounds for moments and tails of random quadratic forms (random chaoses of order ), generated by independent symmetric random variables such that $\lVert X \r…
Two-sided moment estimates for a class of nonnegative chaoses
Rafał Meller
We derive two-sided bounds for moments of random multilinear forms (random chaoses) with nonnegative coeficients generated by independent nonnegative random variables which s…
Extremal particles in branching processess
Rafał Meller
The purpose of this study is to investigate two related spatial branching models with the unbounded branching intensity. The objective is to describe the asymptotic behaviour of th…