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Activities

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Colloquium
Beginning2018-10-15 16:00:00
Ending2018-10-15 17:00:00
Event titleColloquium-Random Weighted Shifts
Speaker方向 教授 (國立中央大學)
PlaceLecture Room B, 4th Floor, The 3rd General Building
DescriptionClick here to read
Attached file File download Adobe PDF
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NoteAbstract
This talk represents some of our initial efforts to develop
what we call a non-selfadjoint version of random operator theory. It is well known that, on finite dimensional vector spaces, random matrix theory has evolved into a remarkably sophisticated subject. On infinite dimensional spaces, most works on random operators so far are restricted to the selfadjoint case, such as random Schrodinger operators. A non-selfadjoint theory is largely missing so far. We
seek to understand the random counterpart of a canonical
non-selfadjoint operator, namely, the unilateral shift, defined as

$$Te_n=e_{n+1}, \quad n=1, 2, \cdots,$$

where $\{e_n\}_{n=1}^\infty$ is an orthonormal basis for a separable complex Hilbert space. This seemingly naive operator encompasses a broad range of beautiful theorems, especially in its connection to complex analysis. Our goal is to consider its random counterpart:

$$Te_n=X_ne_{n+1}, \quad n=1, 2, \cdots,$$

where $\{X_n\}_{n=1}^\infty$ is a sequence of i.i.d. random variables.
This clearly fundamental model seems to elude investigation in the literature so far.
Last Update Time2018-10-01 09:42:39
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