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Results tagged with reference-request
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user 25437
This tag is used if a reference is needed in a paper or textbook on a specific result.
32
votes
3
answers
12k
views
What is the Katz-Sarnak philosophy?
It has been recently mentioned by a speaker (his talk is completely not relevant to random matrix theory/RMT though) that modern statistics, especially random matrices theory, will help solving some n …
- 8,071
7
votes
0
answers
270
views
Relations between Betti numbers for clique complex
Given a clique complex $K$ constructed from a discrete set of vertices (i.e. its faces are isomorphic to the set of cliques in the 1-skeleton of $K$.), it seems that the Betti numbers $\beta_k$ define …
- 8,071
1
vote
Bounding the "spikiness" of a probability distribution
Non-Gaussianness is an ambiguous concept. In the continuum of
probability distributions such as the uniform, where all events are
clustered into a given range and equally likely. On the other s …
- 8,071
2
votes
Accepted
Does Irreducibility holds for the Ergodic non-stationary Markov chain?
Generally, i want to know what are the main differences between
Ergodicity of a stationary Markov chain and non-stationary one?
This question could be a better question if formulated better.
( …
- 8,071
2
votes
Accepted
Expand the pdf of Wishart distribution into power series via orthogonal polynomials
Note that the Laguerre orthogonal polynomials are in form of [1](bearing combinatoric interpretation) and [3]
\begin{align}
& L_n^\nu(x)=(-1)^n\sum_{m=0}^n \binom n m
\prod_{i=1}^m (\nu+2(n-i))(-x)^{ …
- 8,071
4
votes
Wiener Measure measure on functions?
The trick is to regard the Wiener measure as a random sample function $f(x,t)$ where $x\in (\Omega, \mathscr{F},P)$ and $t\in \mathscr{T}$ is the time index set. Then the whole stochastic process can …
- 8,071
4
votes
Accepted
Square integrable conditional expectations as projections
No. Vector space structure is not enough, we actually need a compatible lattice structure to make things work. To apply the conditional expectation operator $E(\bullet\mid Y)$ onto the Hilbert space c …
- 8,071
3
votes
Looking for a certain kind of a distribution
(1) supported on half planes of $\mathbb{R}^n$, you may want to look at folded Gaussian distributions.
(2) supported on a compact surface like $\mathbb{S}^n$, you may want to look at projected Gaussi …
- 8,071
1
vote
Solution to semilinear heat equation at $t=0$: $u_t(0,x) - \Delta u(0,x) + f(x,u,u_x)= 0 \ ?$
This is a well known result from diffusion PDE theory. For example [1] studied the semi-linear equation in form of
$$u_t - \Delta u + u^\gamma = 0, \quad (t,x) \in (0,T) \times \mathbb{R}^n, \gamma> …
- 8,071
2
votes
Weak convergence for discrete-time processes using characteristic functions
If the process you concern is a harmonizable process then Bochner Theorem can be easily generalized into discrete time case by regarding it as Fourier representation. And in some more specific cases D …
- 8,071
18
votes
Manifold of probability measures: connections between two types of metrics
In response to the critical comments below I revised my answer. Hope this is more helpful!
(1) Two kinds of metrics are defined on generally different spaces.
It is not fair to compare these two met …
- 8,071
5
votes
Accepted
Does MCMC overcome the curse of dimensionality?
You need a global convexity to enjoy the optimal convergence rate, otherwise even local convexity will almost surely(not in probabilistic sense) lead to the worst rate you pointed out.
MCMC(Markov Ch …
- 8,071
1
vote
Can we find an Stein operator characterizing a distribution without density function?
The answer is yes. Stein operator is essentially no more than a differential equation $E$(written as an operator notation) which characterized a distribution $f$ as its unique solution. That is the re …
- 8,071
3
votes
Relation between Legendre and Chebyshev polynomials
On pp.13~15 of Fox, L. Parker. Chebyshev polynomials in numerical analysis. No. 519.4 F6. 1968., especially (64)(65), we can see the arguement. As an approach to the minimax solution to the function $ …
- 8,071
7
votes
A Point-free probability theory?
I do not think the accepted answer is a complete one. To be honest there is no such a pointless theory as far as I know.
And I actually have read the book [Kappos] which could be viewed as a continut …
- 8,071