Philipp Tuchel

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20242026

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math.PR2026

Mod-phi convergence for random variables with cyclotomic generating functions

Christoph Thäle, Philipp Tuchel

We consider a sequence of discrete random variables whose generating functions are polynomials only having roots on the unit circle in the complex plane. For such sequences we prov…

math.PR2026

Large deviations for sums of multivariate stretched-exponential random variables: the few-big-jumps principle

Nina Gantert, Joscha Prochno, Philipp Tuchel

Large deviations for sums of i.i.d.\ random variables with stretched-exponential tails (also called Weibull or semi-exponential tails) have been well understood since the 60's, goi…

math.PR2025

Large and Moderate Deviations for Entries of Orthogonal Matrices and the Stiefel Manifold

Philipp Tuchel

Let $A_{N}$ be distributed according to the Haar probability measure on the orthogonal group $O (N)$ for each $N \in N$ . It is well-known that the upper left $m_N\tim…

math.PR2024

Limit Theorems for the Volume of Random Projections and Sections of $ℓ_{p}^{N}$ -balls

Joscha Prochno, Christoph Thaele, Philipp Tuchel

Let $B_{p}^{N}$ be the $N$ -dimensional unit ball corresponding to the $ℓ_{p}$ -norm. For each $N \in N$ we sample a uniform random subspace $E_{N}$ of fixed dimension $m\i…

Mod-phi convergence for random variables with cyclotomic generating functions

Large deviations for sums of multivariate stretched-exponential random variables: the few-big-jumps principle

Large and Moderate Deviations for Entries of Orthogonal Matrices and the Stiefel Manifold

Limit Theorems for the Volume of Random Projections and Sections of ℓpN​-balls

Limit Theorems for the Volume of Random Projections and Sections of $ℓ_{p}^{N}$ -balls