I am primarily interested in random walks on random media, particularly those relating to random trees and random maps. So far, I have mainly been researching these using resistance growth techniques, applied specifically to the case of diffusions on stable looptrees. We now hope to use this as a basis to study random walks on more complicated random objects.
In my first year at Warwick I also worked on a research study group on stochastic integrable systems with George Vasdekis and Stephen Pidgeon, supervised by Prof. Nikos Zygouras and Dr. Yacine Barhoumi. We studied KPZ properties of domino growth models using bijections between domino configurations and a special class of polynomials.
As an undergraduate I also completed a summer research project jointly with Igor Spasojevic on collisions of random walks, supervised by Dr. Perla Sousi. We proved some partial results on robustness of the infinite collision property on recurrent graphs.
I am also starting to work on random loop soup models and their universality properties.
Random Walks on Looptrees and Related Problems, Saint Flour Summer School, July 2018
Random Walks on Looptrees and Related Problems, UK Joint CDT Colloquium, University of Oxford, April 2018
Volume Growth and Heat Kernel Estimates for Stable Looptrees (poster), UK Easter Probability Meeting, University of Sheffield, April 2018
Random Walks on Fractals, Postgraduate Seminar, University of Warwick, October 2017
Events Attended/Research Visits:
48th Probability Summer School, Saint Flour, France, July 2018
Visit to Kyoto University, May/June 2018, supported by GBSF
UK Joint CDT Colloquium, University of Oxford, April 2018
UK Easter Probability Meeting, University of Sheffield, April 2018
Probabilistic Approaches in Mathematical Physics, Summer School, Basque Centre for Applied Mathematics, Bilbao, July 2017
Recent Progress on the Geometry of Random Walks (Peter Whittle Colloquium), University of Cambridge, May 2017
Teaching Assistant for ST202 Stochastic Processes, Term 2 2017/18
Teaching Assistant for ST116 Mathematical Techniques, Term 1 2017/18
Teaching Assistant for MA258 Analysis III, Term 1 2017/18
GCSE Difficulty Judge for Ofqual, intermittent since 2017
A level tutor, academic year 2015/16
Student STEP Mentor at University of Cambridge Study School, April 2014
I also attend and regularly present in the Probability Reading Group, and at the annual MASDOC Retreat.
I can be contacted via email at E.Archer.firstname.lastname@example.org and my office is B0.24.