MathOverflow

Let $0<u<v<k,$ $u+v >1,$ and $k\geq 2.$ Let $X_k^p, Y_k^p$ be iid binomial random variables with parameters $k$ and $p$. Let,
\begin{align*}f_k(p) &= Pr(v X_k^p + v Y_k^p \geq k),\\g_k(p) &= Pr(u X_k^p + v Y_k^p \geq k).\end{align*}...

Let $(\Omega, \mathcal{F}, \mathbb{F}, \mathbb{P})$ be a filtered probability space with $\mathbb{F}=(\mathcal{F}_t)_{0\le t\le ∞}$.
Denote by $\mathcal{F}^{\mathbb{P}}$ the $\mathbb{P}$-completion of $\mathcal{F}$ and by $\mathbb{F}^{\mathbb{P}}=(\mathcal{F}_t^{\mathbb{P}})_{0\le t\le ∞}$ the corresponding augmented filtration....

Let $E/\mathbb{Q}$ be an elliptic curve with complex multiplication by the full ring of integers $\mathcal{O}_K$ of an imaginary quadratic field $K$. A classical application of Iwasawa theory in the direction of the Birch and Swinnerton-Dyer conjecture...

This question is cross-posted from MSE, where it hasn't received an answer after two days.
Let $\mathcal{L}$ be a countable language and $M, N$ be two structures over $\mathcal{L}$. Suppose $|M| = |N| = 2^{\aleph_0}$ and they furthermore satisfy the following condition:...