A theorem of Hunter ensures that the complete homogeneous symmetric polynomials of
even degree are positive definite functions. A probabilistic interpretation of Hunter's theorem …

We introduce a family of norms on the complex matrices. These norms arise from a
probabilistic framework, and their construction and validation involve probability theory …

We establish a sharp moment comparison inequality between an arbitrary negative moment
and the second moment for sums of independent uniform random variables, which extends …

We establish a discrete analog of the Rényi entropy comparison due to Bobkov and
Madiman. For log-concave variables on the integers, the min entropy is within log e of the …

Measures of local and global spatial association are key tools for exploratory spatial data
analysis. Many such measures exist including Moran's I, Geary's C, and the Getis–Ord G and …

We establish a reversal of Lyapunov's inequality for monotone log-concave sequences,
settling a conjecture of Havrilla–Tkocz and Melbourne–Tkocz. A strengthened version of the …

The wild bootstrap is a nonparametric tool that can be used to estimate a sampling
distribution in the presence of heteroscedastic errors. In particular, the wild bootstrap …

We prove Khinchin-type inequalities with sharp constants for type L random variables and
all even moments. Our main tool is Hadamard's factorisation theorem from complex analysis …

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 1/2 fraction of their …

We establish a sharp comparison inequality between the negative moments and the second
moment of the magnitude of sums of independent random vectors uniform on three …