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 Yearling
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Aug
4
awarded  Yearling
Apr
1
comment Finding functions from a series
I disagree, for instance, if $z=-1$ then this series converges to $1$.
Mar
30
comment Integration over Haar Measure
Dear user146290, provided that $f$ is positive or Integrable with respect to the product measure for any $X$ and $Y$ you can use the Fubini-Tonelli Theorem to compute this double integral by computing the iterated integrals, in any order you want. You could, for example, integrate over O(m) and then over O(n).
Aug
4
awarded  Yearling
Jul
2
awarded  Curious
Jul
1
revised Independence of Random Variables and Distribution Functions
A mistyping correction on the first equality.
Jul
1
suggested approved edit on Independence of Random Variables and Distribution Functions
Jun
26
revised Nowhere dense set with positive Lebesgue measure
edited body
May
14
awarded  Nice Question
Apr
17
awarded  Nice Answer
Oct
13
comment Show convergence in probability
Hi Jack, I do not mean your hypothesis implies that $X_i$ have finite first moment, I just give you the argument in this case.
Oct
13
comment Recurrence for dependent random walks.
Yes I decided to rewrite in order to match your answer.
Oct
13
comment Recurrence for dependent random walks.
I changed the question. Because the first version of it was not clear and it seems that I need to be more precise about what kind of dependence I want to consider. Thanks again.
Oct
13
revised Recurrence for dependent random walks.
Change in the dependence type.
Oct
13
accepted Recurrence for dependent random walks.
Oct
13
comment Recurrence for dependent random walks.
Byron, thanks a lot for the comments and answer. You absolutely right if the steps $\{X_1,X_2,\ldots\}$ are independent. Unfortunatelly I poorly stated my problem. What I really wanted is to assume that the steps are dependent, for example, each coordinate is a Ising spin random variable interacting via an infinite range potential. In fact, I should make more precise the dependence, but I thought that this speed $cN^2$ it was enough to conclude transience independently of the type of the dependence.
Oct
12
answered Show convergence in probability
Oct
11
comment Recurrence for dependent random walks.
Dear Byron, thank you for the answer. One more question: to conclude that this random walk is transient did you use some Ergodic theorem (which I guess in my case do not holds) or SLLN ( which probably holds) ?
Oct
11
comment Recurrence for dependent random walks.
Sorry Byron, should be "some" isntead of same.
Oct
11
revised Recurrence for dependent random walks.
edited body