# natema

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bio website location age 25 member for 3 years seen Mar 1 at 2:41 profile views 110

Phd student in Computer Science at Sapienza UniversitÃ  di Roma.

# 159 Actions

 Feb23 awarded Yearling Jul17 awarded Notable Question Jul11 comment What is meant by “constant” in the optional stopping theorem? Is the optional stopping theorem still true with a definition of stopping time that allows it to be infinite? I think no: let the random walk stop moving as it reaches $m$ or $-m$, but define the stopping time to be the time it reaches $m$; this stopping time is infinite but if we could use part (c) we got a contradiction. Jul10 comment What is meant by “constant” in the optional stopping theorem? Thank you! I did not encounter that definition of stopping time before (I'm in the "some cases" of the Wikipedia definition en.wikipedia.org/wiki/Stopping_time#Definition). Jul10 accepted What is meant by “constant” in the optional stopping theorem? Jul10 asked What is meant by “constant” in the optional stopping theorem? Apr22 awarded Tumbleweed Apr15 asked Some questions about a “relaxed” invariant probability problem $|\mu(P-I)|\leq \epsilon$ Feb23 awarded Yearling Jan29 accepted How to formally write a property of a specific coloring of a graph. Jan28 asked How to formally write a property of a specific coloring of a graph. Dec2 awarded Analytical Dec2 accepted On the meaning of the equal sign when used to define the event of a r.v. taking some value. Dec2 comment On the meaning of the equal sign when used to define the event of a r.v. taking some value. @MichaelHardy sorry, I rewrote $\{\omega : X(\omega)=k-Y\}$ without noticing to become redundant. Dec2 asked On the meaning of the equal sign when used to define the event of a r.v. taking some value. Nov30 comment Estimate the density function of a distribution based on binomial distributions. It seems to me that the problem could be stated within a simpler equivalent scenario: we toss $K$ red coins and $I$ blue coins that follow a Bernoulli$(\frac{c}{n})$ and ask what is the probability that the red heads are more than the blue ones. Then, if the two numbers are called $X$ and $Y$, I want the probability that $X-Y$ is positive. I've tried to get the density using characteristic functions but I'm not able to calculate the inverse Fourier Transform (maybe it's a silly approach 'cause give a worse problem than estimating the formula we start with). Do you have further suggestions? Nov30 awarded Benefactor Nov30 accepted Estimate the density function of a distribution based on binomial distributions. Nov30 comment Estimate the density function of a distribution based on binomial distributions. I've already analysed the case where a node gets a certain colour iff it is the only colour it sees, that is a stronger'' case you use to give bounds. I was interested in something finer (a better approximation of the given formula), however you're question is the only that gives a valid approximation and the bounty is expiring, than I thank you very much for your effort. Nov29 comment Estimate the density function of a distribution based on binomial distributions. @Yury, you say that we'll have (approximately) $cI$ and $cK$, but it seems to me that these values should turn out to be weighted as $\frac{c}{n^\epsilon}I$ and $c\frac{n^\epsilon-1}{n^\epsilon}K$. Shouldn't they?