Dear Colleagues and Students,
You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.
Speaker: Gökhan Yıldırım (Bilkent)
“A one-dimensional probabilistic packing problem”
Abstract: Consider n molecules lined up in a row. From among the n – k + 1 nearest neighbor k-tuples, we select one uniformly randomly and bond the k molecules together. Then from the remaining nearest neighbor k-tuples, we select one uniformly randomly and bond the k molecules together. We continue this way until there are no nearest-neighbor k-tuples left.
Let M(n;k) denote the random variable that counts the number of bonded molecules, and let E[M(n;k)] denote the the expected value of M(n;k).
I will present the proof of the following result by R. G. Pinsky :
E(M(n;k))/n converges to an explicit constant p(k) as n tends to infinity.
The result for k = 2 goes back to an article in 1939 by Paul Flory, 1974 Nobel Laureate in Chemistry.
Some open problems will be discussed at the end of the talk. R. G. Pinsky. Problems from the Discrete to the Continuous-Probability, Number Theory, Graph Theory, and Combinatorics, Springer.
Date: October 7, 2019
Place: SA – Z18