307 reputation
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bio website math.ucsd.edu/~jpascoe
location University of California, San Diego
age 24
visits member for 1 year, 6 months
seen 48 mins ago

I am a graduate student at University of California, San Diego under the advice of Jim Agler.


Sep
17
comment Does this simple inequality have a name?
I guess this is equivalent to the inequality $x^2 \leq x(m+M) - Mm,$ since it must be true term by term ($n=1$ case seems to imply the claim in general). So that inequality might have a name if such a thing exists. The fact that $M \geq x$ then immediately implies the claim, so it might not, because it could be seen as being too easy, since it doesn't seem like there's any trick.
Sep
7
accepted Moments of the trace of orthogonal matrices
Sep
6
awarded  Autobiographer
Sep
5
comment Moments of the trace of orthogonal matrices
This is an amazing amount of data. I wonder if it's in any of the triangles in the OEIS (Like Pascal's triangle or Stirling numbers.)
Sep
5
awarded  Nice Question
Sep
5
awarded  Curious
Sep
4
revised Moments of the trace of orthogonal matrices
edited body
Sep
4
comment Moments of the trace of orthogonal matrices
I don't really know what you mean by $A'$ above, nor do I know enough about the values of zonal polynomials. However since I think I am calculating $E_X[\text{tr}(X)^k]$ in your language, is it the case that we will have some cancellation in this formula (the $\lambda$ might cancel the zonal polynomial factors out, but I don't know what you mean by scaling)? (Also in the denominator do you mean $(2k)!$ or $2(k!)$? I guess there's also a similar question about the numerator.)
Sep
4
comment Moments of the trace of orthogonal matrices
Thanks. This is the formula I spotted. However, I want a formula for that holds for large $k,$ (in some sense the $n$ I am choosing is small and fixed) for example if $n=3.$ The above formula doesn't give me enough information.
Sep
4
asked Moments of the trace of orthogonal matrices
Aug
19
comment Is there an algebraic number that cannot be expressed using only elementary functions?
In your post on stackexchange you allowed $i,$ and other elemenary complex analysis: do you still want to do this? It seems if you include integration, it would be possible to express any algebraic number this way. Anyway for an algebraic number $a$ with minimum polynomial $p,$ $a = \int_{\gamma} \frac{zp'(z)}{p(z)} dz,$ where $\gamma$ is a circle with rational radius and center, containing $a$ and no other roots of $p.$
Aug
7
comment Invertibility of random Vandermonde matrix
Yeah, you definitely need to use non-atomicity. I think you need something a bit stronger, since if the points lie in certain varieties, you may run into trouble.
Aug
7
answered Invertibility of random Vandermonde matrix
Aug
4
comment What summations of elementary trig functions are known to have (elementary) closed forms?
If you mean $\Sigma^{\infty}_{k=0} \tan{k},$ I think that sum does not converge. Can you be more explicit about what sums you're talking about?
Aug
3
comment largest eigenvalue of a symmetric matrix
I mean $I$ to be the N by N identity matrix.
Aug
3
comment largest eigenvalue of a symmetric matrix
Then it would seem that taking $\Phi = -I$ and $P = I,$ where I, would imply that the phenomenon is indeed a coincidence. Although, with some extra special structure, the phenomenon may hold.
Aug
3
comment largest eigenvalue of a symmetric matrix
What is $\Phi?$
Jul
31
awarded  Enlightened
Jul
31
awarded  Nice Answer
Jul
31
awarded  Yearling