Sam Thomas // Personal Homepage
Here you can find my publications and what I'm working on, among other things.
I'm doing my PhD with Perla Sousi. My general area of interest is in mixing times of discrete Markov chains.
In particular, I have worked on random walks on random environments.
I am now looking at the uncovered set of a random walk.
Additionally, I have interest in stochastic networks and their applications, for example random access schemes for resource sharing.
My email address is firstname.lastname@example.org
Given that I am currently on the market for a postdoc position, I would be remiss not to include
my CV (last updated 29/12/2019),
my Research Statement (last updated 30/12/2019)
my Teaching Statement (last updated 28/11/2019).
Publications / Work in Progress
So far, I have collaborated, or am collaborating, with the following people:
Cutoff for Random Walk on Dynamical Erdos-Renyi (with Perla Sousi) -- arXiv version (12/08/2018), or latest version (19/03/2019)
- Random Cayley Graphs: Three Paper project (with Jonathan Hermon)
Random Cayley Graphs I: Cutoff and Geometry for Heisenberg groups -- arXiv version (07/11/2019) or latest version (07/11/2019)
Random Cayley Graphs II: Cutoff and Geometry for Abelian groups -- arXiv version (07/11/2019) or latest version (07/11/2019)
Random Cayley Graphs III: Wilson's Conjecture, Cutoff for All Abelian Groups and Spectral Gap -- available imminently
Chen--Stein Method for the Uncovered Set of Random Walk on Znd for d ≥ 3 (with Perla Sousi) -- arXiv version (13/11/2019) or latest version (13/11/2019)
- Loss Network with Alternative Routing: Fast Mixing or Metastability According to Traffic Ratio (solo) -- final stages
- Multicoloured Hardcore Model: Fast Mixing Leading to Short and Stable Transmission Queues (solo) -- final stages
- Limit Profiles for Various Card Shuffles (with Evita Nestoridi)
- Cutoff for Random Walk on Perfect Matchings (with Perla Sousi)
- Contact Process in Dynamical Random Environment (with Domink Schmid)
Academic Visits (Past and Future)
- Aug 2019; Munich (TUM), working with Dominik Schmid (and Nina Gantert)
- Feb 2019; Leiden, working with Frank den Hollander, Luca Avena and Hakan Guldas
- Jan 2019; Eindhoven (TU/e), working with Remco van der Hofstad
Invited Talks (Past and Future)
- May 2020; Recent Progress on Random Walks Conference; CIRM, Marseilles, France
- Sept 2019; Roma Tre Probability Seminar; Rome, Italy
- Aug 2019; Munich (TUM) Probability Seminar; Munich, Germany
- Mar 2019; Young European Probabilists (YEP) Conference; Eindhoven, NL
- Feb 2019; Leiden Probability Seminar; Leiden, NL
- Jan 2019; Eindhoven (TU/e) Probability Seminar; Eindhoven, NL
- Oct 2018; Cambridge Analysts' Knowledge Exchange (CAKE) Seminar; Cambridge, UK
- Feb 2018; Warwick Combinatorics Seminar; Warwick, UK
- Nov 2017; Cambridge Analysts' Knowledge Exchange (CAKE) Seminar; Cambridge, UK
- Sept 2017; Young European Probabilists (YEP) Conference; Eindhoven, NL
I have done supervisions (primarily for my college, St John's) and examples classes for various courses, as listed below.
- Part III
- 2019/20, Mixing Times for Markov Chains
- 2018/19, Percolation and Random Walks on Graphs
- 2017/18, Percolation and Random Walks on Graphs
- Part II
- 2019/20, Mathematics of Machine Learning
- 2018/19, Applied Probability
- Part IB
- 2018/19, Markov Chains
- 2017/18, Markov Chains
- Part IA
- 2017/18, Analysis I
- 2016/17, Analysis I
I have also helped run the St John's STEP School (a weekend in April) in 2015, '16, '17 and '18.
- 2017--current: PhD, University of Cambridge
- 2015--2016: Part III, University of Cambridge
- 2012--2015: BA, University of Cambridge