MathOverflow

I’m looking for a reference for the following result: If $\newcommand{\C}{\mathcal{C}}\C$ is a regular category in which all reg epis split (equivalently, all objects are (regular-)projective, aka the regular axiom of choice), then the ex/lex and ex...

Given an algebraic variety $X$ over a field $k$, a stratification$$\emptyset = X_{-1} \subset X_0 \subset X_1 \subset \dotsb \subset X$$so that $X_i \subset X_{i+1}$ is a closed immersion, and a quasi-coherent sheaf $\mathcal{F}$ over $X$, I am looking...

Let $n \to \infty$ and let $k \ge 1$ be fixed (independent of $n$). Set $d = 2^n$, and let$$(\mathbb C^2)^{\otimes n} \cong \mathbb C^d$$be the Hilbert space of $n$ qubits.
Let $P_k$ denote the set of all non-identity $n$-qubit Pauli strings (tensor products of $\{I,X,Y,Z\}$) of weight at most $k$, i.e. acting nontrivially on at most $k$ qubits. Then$$|P_k| \sim c_k n^k$$for some constant $c_k>0$ depending only on ...

Let $(W_t)_{t \ge 0}$ be a Brownian motion in $\mathbb{R}^n$ with its natural filtration, and let $E \subset \mathbb{R}^n$ be a closed set. Define the hitting time$$\tau_E := \inf \{ t \ge 0 : W_t \in E \}.$$
To show that $\tau_E$ is a stopping time, we often write:$$\{\tau_E \le t\} = \bigcup_{s \le t} \{ W_s \in E \} = \bigcup_{q \in \mathbb{Q}, q \le t} \{ W_q \in E \}.$$...