Dear Colleagues and Students,<\/p>\n
You are cordially invited to the Analysis Seminar organized by the Department of Mathematics.<\/p>\n
Speaker: G\u00f6khan Y\u0131ld\u0131r\u0131m (Bilkent)<\/p>\n
\u201cA one-dimensional probabilistic packing problem\u201d<\/p>\n
Abstract: Consider n molecules lined up in a row. From among the n \u2013 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.<\/p>\n
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).<\/p>\n
I will present the proof of the following result by R. G. Pinsky [1]:<\/p>\n
E(M(n;k))\/n converges to an explicit constant p(k) as n tends to infinity.<\/p>\n
The result for k = 2 goes back to an article in 1939 by Paul Flory, 1974 Nobel Laureate in Chemistry.<\/p>\n
Some open problems will be discussed at the end of the talk.<\/p>\n[1] R. G. Pinsky. Problems from the Discrete to the Continuous-Probability, Number Theory, Graph Theory, and Combinatorics, Springer.
\nDate: October 7, 2019
\nTime: 14:00
\nPlace: SA \u2013 Z18<\/p>\n","protected":false},"excerpt":{"rendered":"
Dear Colleagues and Students, You are cordially invited to the Analysis Seminar organized by the Department of Mathematics. Speaker: G\u00f6khan Y\u0131ld\u0131r\u0131m (Bilkent) \u201cA one-dimensional probabilistic packing problem\u201d Abstract: Consider n molecules lined up in a row. From among the n \u2013 k + 1 nearest neighbor k-tuples, we select one [\u2026] <\/p>\n