78 citations · 138 across the 27 of their papers we have counts for
5 papers · 1 filter
Mean width of regular polytopes and expected maxima of correlated Gaussian variables
Zakhar Kabluchko, Alexander E. Litvak, Dmitry Zaporozhets
An old conjecture states that among all simplices inscribed in the unit sphere the regular one has the maximal mean width. An equivalent formulation is that for any centered Gaussi…
Convex hulls of random walks, hyperplane arrangements, and Weyl chambers
Zakhar Kabluchko, Vladislav Vysotsky, Dmitry Zaporozhets
We give an explicit formula for the probability that the convex hull of an -step random walk in does not contain the origin, under the assumption that the distribution of…
Correlations between real conjugate algebraic numbers
Friedrich Götze, Dzianis Kaliada, Dmitry Zaporozhets
For denote by the number of ordered -tuples in of real conjugate algebraic numbers of degree and naive height . We show th…
Correlation functions of real zeros of random polynomials
Friedrich Götze, Dzianis Kaliada, Dmitry Zaporozhets
We give an explicit formula for the correlation functions of real zeros of a random polynomial with arbitrary independent continuously distributed coefficients.
Convex hulls of multidimensional random walks
Vladislav Vysotsky, Dmitry Zaporozhets
Let be a random walk in such that its distribution of increments does not assign mass to hyperplanes. We study the probability that the convex hull $conv (S_1, \l…