Gallian, Functional Analysis, and Elementary Probability

Gallian was terrific, as I had expected. He talked about Hamiltonian cycles on a torus. I was able to understand it, which is more than I can say about some of the other talks I have attended.

I’m still not too fond of functional analysis, but at least I have two apparently good books on it to help me out. At least we’ll be back to measure theory (Ergodic theory) next quarter. Labutin determined that one of the problems he had assigned us for homework was in fact false, so he dropped that problem. Eleven to go.

I seem to have failed to solve what looks like a simple probability problem: Suppose an instantaneous event happens (at least once) in a given amount of time with probability p. What is the probability that it happens at least twice? I could come up with no better way of solving it than partitioning the time into n sections and letting n go to infinity. But something went wrong, and I got -infinity, which isn’t good when dealing with probability. Now I have to decide which will taunt me more: the need to learn functional analysis or this simple problem.


About Simon

Hi. I'm Simon Rubinstein-Salzedo. I'm a mathematics postdoc at Dartmouth College. I'm also a musician; I play piano and cello, and I also sometimes compose music and study musicology. I also like to play chess and write calligraphy. This blog is a catalogue of some of my thoughts. I write them down so that I understand them better. But sometimes other people find them interesting as well, so I happily share them with my small corner of the world.
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2 Responses to Gallian, Functional Analysis, and Elementary Probability

  1. Anonymous says:

    uhm.. let there be n subintervals. prob(no event in interval)=(1-p)^(1/n).
    we want prob(0)+prob(1)=((1-p)^(1/n))^n+n*((1-p)^(1/n))^(n-1)*(1-(1-p)^(1/n))= 1-p + n*(1-p)^(1-1/n)*(1-(1-p)^(1/n)). so we want lim n->inf n*(1-(1-p)^(1/n)) = -ln(1-p)
    so prob(2 or more) = 1-(1-p)+(1-p)ln(1-p)=p+(1-p)ln(1-p), methinks

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