Zobrazeno 1 - 10
of 261
pro vyhledávání: '"Tkocz P"'
We extend Bobkov and Chistyakov's (2015) upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based on pointwise estimates on densities of sums of independent random vecto
Externí odkaz:
http://arxiv.org/abs/2406.04200
We establish dimension-free stability of Webb's sharp simplex slicing (1996). Incidentally, we investigate Lipschitzness of volume of hyperplane central sections of arbitrary convex bodies.
Externí odkaz:
http://arxiv.org/abs/2403.11994
We establish a monotonicity-type property of volume of central hyperplane sections of the 1-symmetric convex bodies, with applications to chessboard cutting. We parallel this for projections with a new convexity-type property for Rademacher sums.
Externí odkaz:
http://arxiv.org/abs/2312.13922
We prove that the tail probabilities of sums of independent uniform random variables, up to a multiplicative constant, are dominated by the Gaussian tail with matching variance and find the sharp constant for such stochastic domination.
Externí odkaz:
http://arxiv.org/abs/2305.06235
Publikováno v:
Nauki o Wychowaniu, Vol 19, Iss 2, Pp 190-209 (2024)
W niniejszym artykule omówiono wyniki badań jakościowych, których celem była analiza ujawnianych w reakcji na śmierć bliskiej osoby doświadczeń narratorek i mechanizmów ich radzenia sobie z utratą. Badania dokonano w oparciu o 28 listów,
Externí odkaz:
https://doaj.org/article/2909483fc9d647ecbed15d3ca27179f1
We prove a dimension-free stability result for polydisc slicing due to Oleszkiewicz and Pelczy\'nski (2000). Intriguingly, compared to the real case, there is an additional asymptotic maximiser. In addition to Fourier-analytic bounds, we crucially re
Externí odkaz:
http://arxiv.org/abs/2303.16896
We prove an extension of Szarek's optimal Khinchin inequality (1976) for distributions close to the Rademacher one, when all the weights are uniformly bounded by a $1/\sqrt2$ fraction of their total $\ell_2$-mass. We also show a similar extension of
Externí odkaz:
http://arxiv.org/abs/2301.09380
Suppose that the edges of a complete graph are assigned weights independently at random and we ask for the weight of the minimal-weight spanning tree, or perfect matching, or Hamiltonian cycle. For these and several other common optimisation problems
Externí odkaz:
http://arxiv.org/abs/2211.12348
Ball's celebrated cube slicing (1986) asserts that among hyperplane sections of the cube in $\mathbb{R}^n$, the central section orthogonal to $(1,1,0,\dots,0)$ has the greatest volume. We show that the same continues to hold for slicing $\ell_p$ ball
Externí odkaz:
http://arxiv.org/abs/2211.01986
Autor:
Nayar, Piotr, Tkocz, Tomasz
We survey results concerning sharp estimates on volumes of sections and projections of certain convex bodies, mainly $\ell_p$ balls, by and onto lower dimensional subspaces. This subject emerged from geometry of numbers several decades ago and since
Externí odkaz:
http://arxiv.org/abs/2210.00885