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Bounding second eigenvalue of random rank-1 matrix

Consider a fixed set of $n$ points $\mathcal{X}$ on a bounded domain $\Omega \subset \mathbb{R}^d$ and a rank-1 matrix $\mathbf{R}$ with independent entries $R_{ij} \sim \mathcal{N}(0,\lambda_i/n)$ independently for all $(i,j)$ (so $\lambda_i \in [0,1]$ is fixed).
What are the typical bounds on the second eigenvalue of $\mathbf{R}$ as a function of $n$ and $\Omega$? Do the bounds depend on $n$, $\Omega$, and the $\lambda_i$?
More precisely, do there exist constants $C_1,C_2$ and an explicit function $g(n,\Omega,\lambda_1,\ldots,\lambda_n)$ such that $C_1 \leq \lambda_2 \leq C_2$ on average over all matrices $\mathbf{R}$ with (independent) entries $\mathcal{N}(0,\lambda_i/n)$ for all $i=1,\ldots,n$ and with $\lambda_2 \geq g(n,\Omega,\lambda_1,\ldots,\lambda_n)$?

A:

For $\lambda_i$ fixed, the matrix $\mathbf{R}$ is a random variable with a multivariate Gaussian distribution with non-zero mean, so the eigenvalues are also random variables. However, it will be almost surely independent and not too concentrated around their expectation. This makes $\lambda_2$ have an almost surely

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A:

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Flow type using record fields

I have a function that accepts a record value with unknown size and type, such as
type myRecord = {
a: number,
b: string,
c: any,
d: boolean,
e: any,
};

I can imagine that I could do the following
function d(): myRecord {
return {a: 3, d: 4, e: 4};
}

But, I really want to make the following function, as doing so would allow me to access unknown data using a dynamic type name, i.e.
function d(a: ): myRecord {
return {a: 3, d: 4, e: 4};
}

What I want to do above is to accept a named parameter but make the type of the parameter be determined at runtime depending on the value passed in the parameter.
This raises 2 questions.

Is what I’m asking for possible? I’ve been studying the Typescript documentation but I cannot find any mention of it.
If not, why is this not possible?

A:

Create a type that records an object of generic parameter types, and then make myRecord accept one of those:
type a = { a: number };
type b = { b: string };
type c = { c: any };
type d = { d: boolean };
type e = { e: any };

interface All {
a: a;
b: b;
c: c;
d: d;
e: e;
}

const myRecord: All = {
a: 3,
b: “4”,
c: 5,
d: “42”,
e: 6,
};

(I’ve truncated a lot of the boilerplate here for brevity, but you can see it’s an object with a property of type { a, b, c, d, e }.)

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