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1d
comment Getting a Hermite polynomial expansion of Gaussian with given variance.
WoW! So not just on compact sets but on the entire plane!?
1d
comment Getting a Hermite polynomial expansion of Gaussian with given variance.
Wow! So this is much stronger than just L^2 convergence!? Its not just that the square of the difference between partial sums of the series and the kernel when integrated over all space tends to 0? Its like "for all" pairs of points this converges uniformly on compact sets?
1d
comment Getting a Hermite polynomial expansion of Gaussian with given variance.
And is this a pointwise convergence (uniform on compact sets?) or is this a convergence in the sense of L^2 norm (which is like a convergence on average) ?
1d
comment Getting a Hermite polynomial expansion of Gaussian with given variance.
Thanks! Let me look up that reference! This is particularly confusing because the upper bound on the Hermite polynomials is exponentially diverging and hence I have no intuition for its convergence!
Apr
26
comment Getting a Hermite polynomial expansion of Gaussian with given variance.
Could you kindly explain how does one prove that the Mehler kernel expansion converges?
Oct
5
revised A question about using Herbst' theorem
added 10 characters in body
Oct
5
asked A question about using Herbst' theorem
Aug
27
comment What has “$\delta$ Gromov hyperbolic space” got to do with $\mathbb{H}_n$?
Thanks for the reply! I am thinking of stuff like what is the analogue of Bourgain's theorem here.
Aug
27
comment What has “$\delta$ Gromov hyperbolic space” got to do with $\mathbb{H}_n$?
(1) Could you kindly elaborate on the proof that $\mathbb{H}_n$ is a $\delta$-Gromov hyperbolic? (2) Is there some known embedding of a $\delta$-Gromov hyperbolic metric space into some $\mathbb{H}_n$?
Aug
26
asked What has “$\delta$ Gromov hyperbolic space” got to do with $\mathbb{H}_n$?
Jul
7
accepted Is this a misuse of the term “probability space”?
Jul
7
comment What modification is this of the notion of Renyi divergence?
I am not understanding your definiton. I think X and Y are events and then one should think of P and Q as being random variables mapping the outcomes to real numbers and then define it as, D( P(Y|X) || Q(Y|X) | P_X) := \sum(x in X) P( x) \sum (y in Y) P( y )P( x) log[ ( P( y )P( x) ) / ( Q( y )Q(x) )]
Jul
7
comment What modification is this of the notion of Renyi divergence?
So P and Q are to be thought of as maps assigning a probability to each of these outcomes? P : X x Y -> [0,1] and Q : X x Y -> [0,1] ? So what are the maps $P_X,P_Y, Q_X, Q_Y$ ?
Jul
7
comment What modification is this of the notion of Renyi divergence?
So are X and Y events from a common sigma-algebra on which these two probability distributions P and Q are defined?
Jul
5
comment What modification is this of the notion of Renyi divergence?
And what is the meaning of anything like $D(P \vert \vert Q \vert R)$ ?
Jul
5
comment What modification is this of the notion of Renyi divergence?
This isn't clear. $Q$ is a probability distribution on its own. So basically it is a random variable which is assigning a probability to every outcome in some space. (though $Q$ is not a probability measure because on its own it doesn't know what the "events" are) So what is $Q_{Y \vert X}$? What do $Y$ and $X$ have to be for this to make sense?
Jul
5
revised What modification is this of the notion of Renyi divergence?
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Jul
5
comment What modification is this of the notion of Renyi divergence?
@b yen Can you kindly define this quantity "$Q_{Y\vert X}$" and ``$P_{Y \vert X }$" ? I am unable to see why even your first-line is true. Is that a definition? I can't see it to be following from the definition of Renyi divergence...
Jul
5
revised What modification is this of the notion of Renyi divergence?
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Jul
5
comment Positivity of Renyi Mutual Information
@Avitus Can you give a definition of $P_{(X,Y)}$ and $P_X \times P_Y$ ? I guess both are defined on the space of outcomes $\Omega \times \Omega$ and events $F \times F$ (while $\Omega$ is the outcome space and $F$ is the event space of both $X$ and $Y$)