Pedro

@robjohn A useful fact you may already know: if $M_n$ is the maximum of the $S_k$ up to time $n$, then $M_n\geqslant a$ iff $\tau_a \leqslant n$, where $a > 0$. So alternatively one needs to think about the maximum and minimum processes of the walk.

@leslietownes cambridge.org/core/books/catalan-numbers/…

Indeed, if you look at a coin toss sequence that first hits $1$ at $2j+1$, what you're looking at is at a Catalan path from $0$ to $2j$ among all possible $2^{2j+1}$ paths, plus the condition of going up in the last moment, which immediately gives the answer.

Of course $\mathbb P(\tau \geqslant k) = \mathbb P(\tau_a\geqslant k, \tau_{-b}\geqslant k)$, so one might want to compute a joint distribution. It is known that $\mathbb E(t^{\tau_m}) = f_1(t)^{|m|}$ where $f_1$ is the pmf of $\tau_1$, and this is basically computed with Catalan numbers: if I remember correctly, $\mathbb P(\tau_1 = 2j+1) = \frac{1}{2^{2j+1}} C_j$.

@robjohn Yes.

I know that $\mathbb E(\tau) = ab$, but I couldn't compute its variance.

Now consider $\tau = \min(\tau_a,\tau_{-b})$ for $-b< 0 < a$.

@robjohn Wonder if you'd like to take a stab a this one: let $\{S_n\}$ be a symmetric random walk with $S_0=0$, and let $\tau_a = \min\{ n : S_n = a \}$.

@DanielDonnelly "I don't even know who you are!"

Aha. Thanks!

Ah, perfect.

@Jakobian Yes, this I can show.

...

Ok, now it works.

Hi! Do you remember your field theory? Huh?

How can I deduce from this that $K/\mathbb C$ has trascendence degree $2m-4$ from this?

@Thorgott Funny, I have a question about Plücker coordinates: suppose that we look at the field extension $K/\mathbb C = \mathbb C(p_{ij}) /\mathbb C$. It is easy to see that $\mathbb C(p_{ij},x_1,x_2,y_1,y_2) = \mathbb C(x_1,\ldots,x_m,y_1,\ldots,y_m)$ which means that the transcendence degree of $K(x_1,x_2,y_1,y_2)/\mathbb C(x_1,x_2,y_1,y_2)$ is $2m-4$.

@LuckyChouhan No. Why do you ask?

Well, I never left the site!

Does this process have a name?

I am aware of the inverse sampling from a uniform distribution, i.e. that $F_X(X)$ is uniformly distributed for any continuous $X$. Perhaps it is something along these lines?

Maybe there's a probabilist in the chat: I have a uniform distribution into $n$ boxes that fills box $i$ with $k_i$ balls with probability $1/n$. Thus, after say $N$ trials, I would expect about $k_iN/k$ balls in the $i$th box where $k = \sum_i k_i$. It looks like if I let $p_i = k_i/k$ and give box $i$ a probability of $p_i^{-1}/ \sum p_i^{-1}$, I end up with a uniform distribution where each box gets filled with one ball. That is, after $N$ trials, I should expect $N/n$ balls per box.

Please avoid any further discussion, and definitely avoid over-editing. Bye!

Please raise a flag. We'll take a look.

@ArturoMagidin I suspected something like this...

What is the point of changing the indexing from $a_i$ to $b_j$? What is the relation between $i$ and $j$ here?

I am not sure it will be a good use of our time to keep discussing this. Have a good end of the weekend. Bye!

I even wrote "...(agreeably) controversial action to edit...".

@Gokuカカロット I think we already went over this.

@Gokuカカロット ¯\_(ツ)_/¯

You are painting somewhat of a black and white picture which is definitely not the case, as this whole discussion showed.

I do not understand your point, since clearly I have for example agreed with what multiple users have put forward here, including mechanodroid, Elliot Yu and the original poster themselves.

@Gokuカカロット Are moderators and high reputation users not part of the community?

@mechanodroid I do not know why the action was taken, but I do not think the reason for deletion is what you suggest.

At any rate, you are free to flag that answer or any other answer you may deem inappropriate and the moderator will look at it carefully.

@mechanodroid Although I agree that the answer you linked to is also borderline (and that one could not give it as an example in class), I also think that the original question is not a great question to be asking (and is somewhat there for the sake of entertainment, except for a few good honest answers it got). I think the main issue that arose with Andrea's answer is not present. Namely, it seems to me that "relation" is innocuous when it comes to gender or any other aspect of sexuality.

@mechanodroid What kind of similarities?

It looks like it was deleted by a community manager.

@ElliotYu Yes, I agree with your last comment. The reason I would have deleted the answer is because it is not suitable for the site nor for the question that was made (also somewhat unsuitable). I think there was no intent to slap any hands on Alexander's part, and he just aimed to make a compromise: the answer had many upvotes but the way the anecdote/joke was phrased raised some flags. I did not even think that the OP's grievance could be centered around the impression that a moderator was contesting the gender of a person in their anecdote, but this was never the case.

@ElliotYu I am not contesting that, and do not think the reason why the gender was removed is because it was up for debate. The point was that the answer was creating flags because of the reasons mentioned by Alexander, and a compromise was to make the joke genderless. After all, the essence of the "joke" (that using linear algebra as a pick up strategy is quite silly) was preserved.

@ElliotYu It's good to know that we have the same opinion. (Regarding your comment about the dictionary: I did find "an account regarded as unreliable or hearsay"? I am not sure this path will lead us anywhere useful. My point is that an anecdote has a non-trivial component of subjectivity, and this is what created the issues here.)

Thus, I am not contesting what the OP perceived, but rather trying to put in perspective that different people witnessing the interaction might have reacted in a different way, and may not have found the interaction funny, nor the suggestion to go around "picking up girls at a bar" with linear algebra, thus explaining the flag. Personally (I thought I had written it already but it seems not) I would have simply deleted the "joke/answer" as it was not serious and moved on, but I can understand the point of view of the flagger.

@ElliotYu I am simply trying to emphasise the subjective point of view of the poster/observer. What seems to have triggered the flag and the subsequent (agreeably) controversial action to edit the answer is that in pick-up situations, the experience of the receiving party and a random observer can vary wildly, and making the situation into a joke might have ruffled some feathers, especially in male dominated STEM fields like mathematics. For example, the person doing the picking up may be enjoying their lines but the person on the receiving end might be uncomfortable. (cont'd)

@AlexM. I do not agree. I am engaging with some of the points made by the user which support their point of view and sharing mine as a moderator. This is made in the context of the edit done by another moderator to give users a broad idea of what we (moderators) think about the actions carried out by a team member. Notice that the user is referring to "facts" in the posts to make their argument, but then saying "our impression" in the comments. Part of my answer is there to point this lack of consistency.

@AndreaMori I do not know what the upvotes meant, especially since the answer is about 10 years old now. Probably some people found the anecdote entertaining, or something along those lines. Regarding the second comment: I am taking the anecdote at face value, and do not think you wrote anything offensive. At most, I think it is unnecessary to post that as an answer, maybe even as a comment, and I just do not find the anecdote entertaining or funny in anyway. For example, I would not tell students that anecdote during a linear algebra class, or during an informal lunch.

@TheAmplitwist Definitely related. The main difference of this post with that post is that "Nancy" was a fictional character, while here the OP argues that what he is talking about is factual (although it is rather more anecdotical, perhaps putting it closer to the situation in that post).

@Gokuカカロット A better move than what?

Your protest to the upvoting suggests a misunderstanding of what people value in a question. This is subjective but you seem to have too much of a rigid opinion of what makes a good question. This is bound to get us to situations like this. I do not think the attitude you are taking (for example, not even acknowledging that the poster is new to the site and trying to help) is useful.

My point is that closing requires a valid reason. You seem to be instructing people to close the question and expecting them to follow suit (it seems they did, giving the close count) without a valid reason. You also do not seem at all interested in helping the OP in improving the question to suit the site better.

In your comment you also mention duplicates. Can you provide a duplicate for this question?