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Results tagged with limits-and-convergence
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user 21753
Convergence of series, sequences and functions and different modes of convergence.
4
votes
0
answers
233
views
Convergence of a particular double sum [closed]
Consider the following double sum:
$$Q(n)=\frac{1}{n^2}\sum_{i=1}^{n}\sum_{j=1}^{n}\left [ \partial _{ij}lnf\left ( x \right ) \right ]^2$$
where $\partial_{ij}$ is the partial second order derivativ …
- 267
1
vote
1
answer
2k
views
Limit of largest eigenvalue [closed]
For positive definite matrix, if we increase the dimension to the infinity, is it true that the largest eigenvalue stays bounded from above?
In other words does the following limit exists:
$$\lim_{n\ …
- 267
2
votes
1
answer
298
views
Convergence of weighted double sum of random variables
I'm looking for convergence results of particular weighted sum:
$$S_n=\frac{1}{n}\sum_{i=1}^{n}\sum_{j=1}^{n}a_{i,j}X_i X_j.$$
when random variables $X_i$ ar i.i.d. Are there any investigation regard …
- 267