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Mathematical Physics Seminar

The truncated moment problem

Location:  Hill 705
Date & time: Thursday, 06 October 2016 at 12:00PM - 12:11PM

Tobias Kuna , University of Reading: Let K be a subset of the real numbers. The (one-dimensional) truncated moment problem on K is to find, for given numbers m_1,...,m_n, a random variable X which takes values in K and whose moments are given by the m_k: E[X^k]=m_k. More accurately, one wants to find necessary and sufficient conditions, in term of the m_k, for the existence of such a random variable. The multi-dimensional version of this problem, in which K is a subset of a Euclidean space of higher dimension, is surprisingly hard and is far from being resolved; we give a short introduction to the problem and to the state of the art.

Finally, we describe a recent result concerning the truncated moment problem for a discrete set in one dimension; this is work in collaboration with M. Infusino, J. Lebowitz, and E. Speer.


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Department of Mathematics

Department of Mathematics
Rutgers University
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