Probability in High Dimension: Suprema

Reading Group – Department of Statistics, University of Oxford

Info

This reading group is focussed on the notes "Probability in High Dimension" by Ramon van Handel. We will read through the second part of the notes which focusses on suprema of random variables. It would be helpful to know the contents of the first part of the notes (in partcular sections 2 and 3), though its not at all necessary. Many of the more relevant results from these sections are covered succinctly in Patrick's notes.

Please contact us via email (tyler.farghly@keble.ox.ac.uk, carlo.alfano@linacre.ox.ac.uk) if you are interested in joining the group, have any questions or have any suggestions.

Notes
Exercise solutions
Agora page
The reading group is no longer running (as from 19/02/21)
Schedule
Week Topic Pages Exercises
1 Finite maxima and covering 113-117, 119-122 (7) 5.1-5.3, 5.6
2 Packing and approximation 123-129 (7) 5.4, 5.5, 5.7, 5.8
3 The chaining method 131-138 (7/8) 5.9-5.10
4 Penalization and the slicing method 140-145 (5) 5.11, 5.15
5 Penalization and the slicing method – 5.12-5.14
Break for the holidays
6 Gaussian processes and comparison inequalities 151-158 (7) 6.1-6.3
7 Chaining in reverse and stationary processes 162-168 (6) 6.4-6.7
8 The majorizing measure theorem 170-178 (8) -
9 The majorizing measure theorem - 6.5, 6.6, 6.9, 6.10
10 The generic chaining and admissible nets 181-187 (7) 6.11