18 problems

Does the Benjamini–Hochberg procedure always control false-discovery rate at its nominal level for correlated two-sided Gaussian p-values?

Does the finite signed basic adjoint relation determine the invariant signed measure uniquely, and how far beyond the Harrison–Reiman class can uniqueness extend?

Can uniform $L^1$ consistency of empirical spatial distribution and depth estimators be proved with a rate independent of the ambient dimension?

Is the density f of argmaxₜ{W(t)−t²}, for two-sided Brownian motion W, strongly log-concave?

Can the qualitative fourth-moment theorem for sums of two Wiener–Itô integrals of different parity be strengthened to an explicit total-variation rate depending only on the fourth…

For the switch–walk–switch walk on $\mathbb{Z}_2\wr\mathbb{Z}$, with starts $x=(\mathbf{0},0)$ and $y=(\mathbf{0},2)$, prove …

For the switch–walk–switch lamplighter walk on $\mathbb{Z}_2\wr T_d$, prove the sharp asymptotic …

If $P_n(z)=\sum_{k=0}^n\varepsilon_kz^k$ has independent uniform signs, does the number $R_n$ of roots in $|z|\leq1$ satisfy $R_n/(n/2)\to1$ almost surely?

Can the limiting position distribution of the canonical one-dimensional particle-swarm optimizer during stagnation be Gaussian?

Does the Gaussian Moments Conjecture hold for complex polynomials in two independent real Gaussian variables?

If all positive moments of a complex polynomial in independent standard Gaussian variables vanish, must every polynomially weighted moment eventually vanish as well?

For iid random signs, does the number $R_n$ of real roots of $\sum_{k=0}^n\varepsilon_kz^k$ satisfy $R_n/\log n\to2/\pi$ almost surely?

What is the optimal universal constant in the thin-shell variance bound for isotropic log-concave probability measures?

Must $\mathbb P(S<\mathbb ES+1)\geq1/e$ hold for every sum of independent nonnegative random variables with $\mathbb E X_i\leq1$?

For nonnegative weights $w_i$ with $\sum_i w_i=1$ and independent $v_i\sim\mathrm{Bernoulli}(p)$, for which $p$ does $\Pr[\sum_i w_i v_i\geq p]\geq p$ hold for every choice of weig…

For every smooth positive density $f$ on $\mathbb{R}^d$, must the Fisher information $t\mapsto I(f*\gamma_t)$ be log-convex along the heat flow?

Must every time derivative of entropy along the heat flow obey the alternating-sign inequalities predicted by the Gaussian completely monotone conjecture?

For i.i.d. Rademacher signs $a_k(t)=(-1)^{\epsilon_k(t)}$, determine the almost-sure order of …