MATH Seminar: “A One-Dimensional Probabilistic Packing Problem,” Gökhan Yıldırım, SA-Z18, 2PM October 7 (EN)

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 [1]:

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.

[1] R. G. Pinsky. Problems from the Discrete to the Continuous-Probability, Number Theory, Graph Theory, and Combinatorics, Springer.

Date: October 7, 2019
Time: 14:00
Place: SA – Z18