I’m a probabilist mainly interested in random discrete structures, with occasional detours into analysis and combinatorics – hopefully the research-centred content of this blog gives a flavour of what I work on.

I am currently a postdoctoral fellow and lecturer in the Probability group at the Department of Statistics in Oxford, where I also act as tutor in Probability for Lady Margaret Hall. I have been co-lecturing the course *SC9: Probability on graphs and lattices*.

I completed my doctoral studies (which Oxford calls a DPhil, not a PhD) in 2016, for which my advisors were Christina Goldschmidt and James Martin and my thesis concerned Self-organised criticality in random graph processes. Following this, I spent 2.5 years working with Oren Louidor and others at Technion, in Haifa, Israel, where I was grateful to be supported by a Cohen-Coleman Fellowship, and given the chance to lecture a cross-faculty graduate course on *Random Graphs and related topics.*

The purpose of this blog has varied over time, especially as the balance of work hours spend reading theory versus writing papers has fluctuated. My goal is to write 1500-2500 words on relevant topics in probability theory or related areas occasionally, with proper statements and references, but without full technical details when appropriate. Good heuristics are the sort of things I tend to forget as months and years go past, and so for my own benefit I focus on those, though perhaps that sometimes works well for other readers too.

In evenings and during holidays, I am also involved in various academic aspects of the UK’s programme for the International Mathematical Olympiad. Posts about competition problems, or motifs in Euclidean geometry are, unsurprisingly, easier to write than posts about topics close to the frontiers of mathematical knowledge, so have, occasionally, somewhat saturated this blog, but you can exclude these by using the categories in the right-hand column, should you wish!

I remain surprised that blogs like this are not so common, and am always happy to talk about my experiences (positive, negative, and neutral – though mostly positive!) and logistic issues with anyone who is interested in starting something similar.

The title of the blog was a consequence of *Almost Sure* and *Almost Everywhere* already being taken as WordPress handles. Unintentionally, it has ended up accurately describing my ambitions regarding visiting other countries. I visited country number 60 (San Marino) just before the first lockdowns of 2020 came into play.

Dominic Yeo

Hi. I have a quick question for you.

I am a PhD student majoring in statistics. Since I took only introductory mathematical analysis course in undergraduate, I have difficulty with understanding probability theory now, especially measure-related theory. Could you give any comment about any books – better for self-study – or a way to improve knowledge of theoretic probability theory?

Try “Probability and Martingales” by David Williams, or “Probability and Measure” by Patrick Billinglsey. Off the top of my head, I believe both are self-contained. The former is quite brief, and the latter extensive; both are excellent, though Billingsley’s text is my personal favourite and is an absolutely famous book.

Wonderful blog