Timeline for Moments of random matrices - when are they finite
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2013 at 9:50 | comment | added | Liviu Nicolaescu | The problem is tricky. Just look at the case when $A$ is diagonal and you se you need to impose some conditions on $A$. My argument shows that a condition of the type $C^2|A| <1$ will do. | |
| Jan 31, 2013 at 6:34 | comment | added | pierre robert | This is essentially the question. What is needed? I need to evaluate the expected inverse of $I+AX$, which I will do through a Neumann series. But the series is not always convergent, and in that case I will use a preconditioned in order to guarantee convergence of the series expansion. The problem is now that I don't really know how to design the preconditioned. | |
| Jan 30, 2013 at 22:31 | comment | added | Liviu Nicolaescu | You need to assume something about $A$. Even the case $N=1$ you can see that if $|A|>1$ the moments go to $\infty$ like $|A|^n$. | |
| Jan 30, 2013 at 22:27 | comment | added | Liviu Nicolaescu | The moments are finite as $n\to\infty$. They may not be bounded as $n\to\infty$. | |
| Jan 30, 2013 at 21:24 | comment | added | pierre robert | It is not entirely clear to me... From your answer it appears as if your conclusion is: They are always finite, no matter what $A$, the variance of $Z$, the mean $\mu$ and $n$ are...But this cannot be true. Also, the constant $C$ is important. If C>1, it is not clear at all to me that the moments are finite as $n$ grows large. I can agree that for finite $n$, the moments are finite, but the question concerns the case whether $$\lim_{n\to \infty} \mathbb{E}(AX)^n=0$$ | |
| Jan 30, 2013 at 20:54 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
added 366 characters in body
|
| Jan 30, 2013 at 19:51 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |