1,259 reputation
812
bio website mat.unb.br/cioletti
location Brasilia, Brazil
age 37
visits member for 3 years, 8 months
seen Mar 27 at 6:07

I am a mathematical physicist at Universidade de Brasília. I am currently interested in Gibbs Measures and Ergodic Theory. Contact: leandro.mat@gmail.com


1d
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
Oct
11
answered What is an example of an open set in $\mathbb{R}^2$ which is a Cartesian product of two non-open sets in $\mathbb{R}$?
Oct
11
revised Recurrence for dependent random walks.
Corrected misprint in the definition of recurrence.
Oct
10
asked Recurrence for dependent random walks.
Aug
4
awarded  Yearling
Aug
4
awarded  Yearling
Jun
15
comment which are positive definite matrix
Yes and worth to mention that in the definition of positivity we only have to verify the inequality for $x\neq 0$.
Jun
15
comment which are positive definite matrix
@Mex Leandro :)
Jun
15
comment Terminology between essentially bounded function and bounded function.
No see the William's answer. It is not possible, in general, to show that $f$ is bounded. Another very simple example can be constructed by using a Dirac delta measure.
Jun
15
answered which are positive definite matrix