Random Matrix Theory

An Induction without Hypothesis

September 21, 2022September 22, 2022

I think Nate and Eli will get this without a lot of background set up. Let $$\omega(x) = \sum_{\mathfrak t : \underline L \nearrow \underline{NL}} \mathrm{Wr}(\mathbf p_{\mathfrak t}; x) \mathbf e_{\mathfrak t} \in \Lambda^L(V),$$ where… Read More »An Induction without Hypothesis

Some Inner Product Calculations

August 17, 2022August 26, 2022

In Nathan Hunter’s thesis, the inner product of two monomials $x^M$ and $x^L$, with $M \leq L$ are given as $$\begin{eqnarray}\langle x^M , x^L \rangle &=& 2 \pi \sum_{n=-NM}^M {M \choose \frac{NM + n}{N+1}} {L… Read More »Some Inner Product Calculations