The spectral-gap tag has no usage guidance.

**19**

votes

**0**answers

769 views

### Could unramified Galois groups satisfy a version of property tau?

This is an experiment: there is a question I want to mention in an article I'm writing, and I am not sure it's a sensible question, so I will ask it here first, in the hopes that if it's insensible ...

**2**

votes

**2**answers

1k views

### Estimating a spectral gap

Suppose you have a real positive definite matrix $A$ who eigenvalues are $\lambda_{1} \leq \lambda_{2} \leq \ldots \leq \lambda_{n}$. I am interested in bounding from below $\lambda_{2}-\lambda_{1}$. (...

**0**

votes

**1**answer

69 views

### Lower bound on Spectral Gap of Rank one + Diagonal

For some $x\in\mathbb{R}^n, \|x\|_2^2=1$ and $\alpha\geq 0$, consider the positive semi-definite matrix
$$
X_\alpha := xx^T + \alpha\sum_{k=1}^nx_k^2e_ke_k^T.
$$
Suppose for simplicity that the ...