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 Yearling
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Dec
26
awarded  Yearling
Dec
24
comment Ergodic means and Birkhoff theorem
Does $\{ a\}$ refer to the fractional part of $a$? I ask because if so then the map you're interested in is en.wikipedia.org/wiki/Irrational_rotation on the unit circle, equipped with Lebesgue measure.
Dec
24
answered evaluate the path integral around a circle in complex plane
Dec
11
comment Show that every Banach space is isometric to a subspace of an $L_{\infty}(\mu)$-space
math.stackexchange.com/questions/112619/…
Jul
1
comment Preservation of Positive-Definiteness from Small Perturbations
@the_elder It would be an interesting question (perhaps you should pose it!) to describe the geometry of the set of perturbations $B$ for which a given "strictly" positive semidefinite $A$ remains positive semidefinite.
Jul
1
comment Preservation of Positive-Definiteness from Small Perturbations
@the_elder No, if $A$ is "genuinely" semi-definite then it possesses a zero eigenvalue, hence a nontrivial kernel, and so is therefore noninvertible. In particular, there exist arbitrarily small perturbations $B$ which 'push' $A$ towards having negative eigenvalues.
Jul
1
comment Preservation of Positive-Definiteness from Small Perturbations
Hah, good catch @the_elder. $\Delta A$ must be hermitian itself before this result can possibly be true.
Apr
6
reviewed Approve What does R^d in last lines refer to
Jan
13
awarded  Nice Question
Jan
12
comment Integrate $\int_C{\tan{z}\ dz}; C: y=x^2$ (complex numbers)
May you use the fact that the quotient of (non-vanishing) analytic functions is also analytic?
Jan
8
revised Find the Fourier integral
added 19 characters in body
Jan
8
comment Find the Fourier integral
Oops, I will correct the error.
Jan
8
comment Find the Fourier integral
@robjohn and my contour encircles precisely one of them.
Jan
7
answered Find the Fourier integral
Dec
26
awarded  Yearling
Dec
8
awarded  Caucus
Oct
24
reviewed Approve Area between curves $y=x^3$ and $y=x$
Oct
22
comment How to adapt the discrete-time to continuous, $(A) \Rightarrow (B)$?
It is a standard and illuminating exercise to carry out this deduction for oneself. Hint: try applying the discrete-time MET to the time-one solution map. Does applying $d\phi^s_x$ for $s \in [0,1]$ affect the asymptotic growth rates of vectors?
Oct
20
reviewed Approve Find Elements of a Quotient Group
Oct
16
comment probability of clusters for iid points
This is to say that the distribution of an $X_i$ depends on $n$ as well, correct? It would be more suggestive to write $X_i^{(n)}$, since you're really thinking of a triangular array of random variables.