11 problems

Let $F_0$ have a continuous positive density $f_0$ on $(0,M)$, where $M>0$, and let $t_0\to(a,b)$ be an interior point. Let $\hat F_n$ be the nonparametric maximum likelihood estim…

Concentration and limiting-distribution conjecture. The measure $\mu_{n,m}$ concentrates around its mean and, up to a suitable normalization constant, admits an asymptotic limiting…

Let $\mathcal F$ be a degenerating family of $n$-dimensional isolated hypersurface singularities: it is equipped with a filter and its Milnor number function satisfies…

Let $\mathbf{Y}_{n}$ and $\mathbf{N}_{n}$ denote the quantities associated with the urn model, and let $\mathbf{H}$ be a homogeneous generating matrix. The asymptotic properties of…

Let $X_{n,k}$ be the fluctuation variable, let $\widetilde\Xi(\gamma_i)$ denote the limiting random quantity associated with a root $\gamma_i$, and let $\Gamma_*$ be the set of rel…

For a Veronese embedding, let a row of its Betti table mean the sequence of Betti numbers with fixed homological or internal degree. Ein–Lazarsfeld normal-distribution conjecture.…

Gaussianity conjecture. The term $U_4$ is asymptotically Gaussian.

Distribution conjecture. For each integer $p$ with $|p|>1$,

Asymptotic absorption-count conjecture. The mean normalized count tends to a constant as $t\to\infty$,

Let $\phi$ be Euler's totient function. For $x\geqslant 1$, let $V(x)$ be the number of totients at most $x$, and for an integer $k\geqslant 1$, let $V_k(x)$ be the number of totie…

Let $f_0$ have $\partial^d f_0(\boldsymbol{x})/\partial x_1\cdots\partial x_d$ continuous in a neighborhood of $\boldsymbol{x}_0$, with … Let…