29 problems

Lin's conjecture. $X_t$ is moment determinate if and only if $X_1^t$ is moment determinate.

A homogeneous process with independent increments is a stochastic process whose increments are independent and whose increment distributions depend only on the length of the time i…

Kuperberg's mixed-base conjecture. There are unique constants

Let $Y$ be an absolutely continuous random variable, and let a linear combination of independent Bernoulli random variables be formed. Kuperberg's moment-matching conjecture. The m…

Log-squared weight conjecture. The weight satisfies

Higher-even-moment collapse conjecture. For the classes $\mathbb{E}X^{2m}\leq\kappa_{2m}$, the one-sided/two-sided collapse of the cited collapse result persists beyond the corresp…

Let $X(cmathbb{R})\subsetcmathbb{R}^2$ be an affine plane cubic whose projective closure has at least two real points at infinity. The preceding example exhibits pathological behav…

Let $\alpha$ be a finite positive parameter, and consider the generalized $\alpha$-unimodal Gauss bound in equation (10) for the worst-case probability of the event…

Müger–Tuset's conjecture. Perhaps

Let $K$ be one of the scalar fields under consideration, and let an optimal measure be a measure maximizing the relevant $q$-th moment among isotropic measures. A support is non-di…

Let $H_N$ be the $N\times N$ Hankel moment matrix generated by the weight $w(x)={\rm e}^{-x^{\beta}}$ on $[0,\infty)$, with $\beta>0$, and let $\lambda_{\min}(H_N)$ denote its smal…

Higher-order moment-ideal conjecture. For $d$ sufficiently large, the ideal $I_{l,d}$ is generated by these polynomials. This generalizes the proposed second-order generators to hi…

Let $I_{2,d}$ be the ideal of moments of the second-order local mixture, with moment variables $M_i$. For integers $i,j$ satisfying … and coefficients … … the relevant degree-$d$ m…

Lin's conjecture. For every $t>0$, $\mathbf X_t$ is MD if and only if $\mathbf X^t$ is MD.

Let $X$ and $Y$ be positive random variables with densities satisfying Lin's condition, and suppose their joint distribution is absolutely continuous. Lin's product conjecture. The…

Let $\omega=\cup_{k=1}^N\omega_k$ be a multiply connected set, where the sets $\omega_k$, for $k=1,\dots,N$, are nonintersecting simply connected open domains with $C^{1,1}$ bounda…

Let $p\geq 3$, and let $\lambda_n$ and $\mu_n$ be birth and death rates that are polynomials of degree $p$ with … … Assume that $1<C-D<p-1$. Valent's conjecture. The order of the c…

Let $\zeta(s)$ denote the Riemann zeta function and define … Here $k$ is a fixed positive parameter and $c_k$ is a constant depending on $k$. Folklore moment conjecture. One has ……

Let $\{F_n\}_{n \ge 1}$ be a sequence of random variables in a fixed Wiener chaos or Wigner chaos of order $p\ge 2$, normalized by … for all $n\ge 1$. In the classical case, let…

Composition conjecture for moments. The moment conditions imply the composition condition: there should exist polynomials $\widetilde F$, $\widetilde G$ and $W$, with $F'=f$,…

For an uncontrolled stochastic problem, assume that all moments are finite. Convergence conjecture. The upper and lower bounds computed by the semidefinite-programming moment metho…

Valent's conjecture. For this indeterminate Stieltjes moment problem, the order, type, and Phragmén–Lindelöf indicator function are

Let $A,B,C,D$ be the entire functions associated with an indeterminate Hamburger moment problem through the Nevanlinna parametrization. Suppose the moment problem has ordinary orde…

Let $\sigma>0$ and set $c=\exp(\sigma^2)$. Let $V$ be the set of probability measures on $[0,\infty)$ that are distributions of nonnegative random variables $X$ satisfying … For…

Let $c=\exp(\sigma^2)$ with $\sigma>0$, and let $\ell(b,c)$ denote the single-orbit discrete distributions supported on $\\{\ldots,b/c^2,b/c,b,bc,bc^2,\ldots\\}$ that have the logn…