High Dimensional Probability X

This volume collects selected papers from the Tenth High Dimensional Probability conference, held from June 12 to 16, 2023 in Bedlewo, Poland. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Topics covered include:

• The Gram-Schmidt walk algorithm;
• Variance bounds;
• Random interlacements;
• Contraction theorems on the half-space.

High Dimensional Probability X will be a valuable resource for researchers in this area.

Chapter 1 Optimal constants in concentration inequalities on the sphere and in the Gauss space. - Chapter 2 Some remarks on the Gram-Schmidt walk algorithm and consequences for Komlos conjecture. - Chapter 3 Some notes on moment inequalities for heavy-tailed distributions. - Chapter 4 Stability of Klartag s improved Lichnerowicz inequality. - Chapter 5 Variance bounds: some old and some new. - Chapter 6 Some obstructions to contraction theorems on the half-sphere. - Chapter 7 Dimension-free comparison estimates for suprema of some canonical processes. - Chapter 8 Sharp phase transitions in Euclidean integral geometry. - Chapter 9 Fourier analytic bounds for Zolotarev distances, and applications to empirical measures. - Chapter 10 A note on the fluctuations of the resolvent traces of a tensor model of sample covariance matrices. - Chapter 11 New Berry-Esseen bounds for random sums of centered random variables. - Chapter 12 The large and moderate deviations approach in geometric functional. - Chapter 13 Random interlacements: the discontinuous case. - Chapter 14 Local moduli of continuity for permanental processes that are zero at zero. - Chapter 15 Estimation of trace functionals and spectral measures of covariance operators in Gaussian models. - Chapter 16 Higher-order perturbation expansions for eigenvalues and eigenprojections I: simple eigenvalues and random perturbations.