Slides from recent talks

Some topics in spatial networks. UNC Chapel Hill Statistics Seminar, and Brown University Applied Mathematics seminar. October 2023.

The Critical Beta-Splitting Random Tree Model: Results and Open Problems. UBC Vancouver Probability Seminar, January 2023; University of Oxford Discrete Mathematics and Probability Seminar, June 2023; 50 Years of Percolation meeting, Cambridge, July 2023; University of Washington Probability Seminar, November 2023. Also this youtube video of the Oxford talk.

Gambling under unknown probabilities as a proxy for real world decisions under uncertainty. Nederlands Mathematisch Congres (via Zoom), April 2021; Columbia University, October 2022.

Open problems within three topics in spatial networks: scale-invariance, the nearest unvisited vertex walk, and a toy model of 4X games. INRIA DYOGENE Seminar, Paris, April 2022.

From Euler to Stellaris: Some of my favorite open problems in probability. Probability, Analysis and Dynamics workshop, Bristol UK, April 2022. Also Version for undergraduates UC Santa Barbara CS Theory seminar, February 2023.

Two processes on compact spaces. CUNY Probability Seminar, October 2021.

Can one prove existence of an infectiousness threshold (for a pandemic) in very general models of disease spread? Duke Probability Seminar, September 2021

The Nearest Unvisited Vertex Walk on Random Graphs. Probability seminar, University of Washington, January 2020; Talking Across Fields (Diaconis birthday), Stanford, February 2020.

Scattered thoughts from applied probability. Distinguished Speaker Seminar, Statistics Dept, Oxford University. June 2019.

Random networks embedded in the plane. Walking through the Brownian zoo: A conference in honor of Jean-Francois Le Gall's 60th birthday, Paris, June 2019.

Two elementary paradoxes. Interacting Particle Systems conference to honor Tom Liggett, UCLA March 2019.

Some of my favorite open problems. Notre Dame Math Colloquium, September 2018. University of Washington, October 2018.

On Martingales, Markov Chains and Concentration. A Symposium on Optimal Stopping, in Memory of Larry Shepp. Rice University, June 2018.

Limits for processes over general networks. Columbia-Princeton Probability Day, April 2018. Stanford probability seminar, April 2018.

Epidemics on general networks: a conjecture. Workshop Network Models: Structure and Function, Oberwolfach, Germany, December 2017..

Elo Ratings and the Sports Model: a Neglected Topic in Applied Probability? Applied Probability at The Rock, April 2017.

Poissonian rain coloring and a self-similar process of coalescing planar partitions. Probability seminar, Berkeley, February 2017 and SouthEastern Probability Conference, May 2017.

A framework for imperfectly observed networks. Simons Institute workshop "Random Instances and Phase Transitions", Berkeley, May 2016. Conference on Random Graph processes, UT Austin, May 2016. Workshop Graph Limits and Statistics, Newton Instititute, Cambridge UK, July 2016. Overlapping version A general SI epidemic and a framework for imperfectly observed networks . Workshop Stochastic models of the spread of disease and information on networks, ICMS Edinburgh, 2016.

Waves in a Spatial Queue: Stop-and-Go at Airport Security. HajekFest, U. Illinois, October 2015. UC Davis, December 2015.

Weak Concentration for First Passage Percolation Times on Graphs and General Increasing Set-valued Processes . Probability seminar, Berkeley, September 2015.

Foundational questions about sports rating models . Limit Theorems in Probability meeting, Imperial College London, and Probability Theory and Combinatorial Optimization meeting, Duke University, both March 2015. Chinese Academy of Sciences, May 2015.

The Compulsive Gambler and the Metric Coalescent. Newton Institute Cambridge, March 2015; Tsinghua University, May 2015. Previous version at Stanford Probability seminar, April 2014 and CRMS Montreal Workshop on Random Trees, August 2013.

Spatial Networks and Probability. Leiden, April 2014; UT Austin, May 2014. UC Davis, April 2015; Peking University, May 2015.

Discrete random structures whose limits are described by a PDE: 3 open problems. Columbia University, April 2014.

Fluctuations of Martingales and Winning Probabilities of Game Contestants. SPA conference, Boulder CO, August 2013.

Exchangeability and continuum limits. Mittag-Leffler Institute, June 2013.

Interacting particle systems as stochastic social dynamics. Tsinghua University, May 2015. CRMS Montreal Workshop on Random Trees, August 2013. Previous versions at U.C. San Diego (April 2013) and U.T. Austin (April 2011).

Entropy for Sparse Random Graphs With Vertex-Names. ITA Workshop, San Diego, February 2013. A previous version was given at BIRS Banff workshop ``Models of sparse graphs and network algorithms", February 2012: here is a video of that version.

A conjectured compactification of some finite reversible Markov chains. Courant Institute, September 2012.

My summer 2012 lectures on Finite Markov Information Exchange Processes have their own page.

Scale-invariant random spatial networks. Berkeley Probability Seminar, September 2010. Canadian Math Society Winter Meeting, Vancouver B.C., December 2010. Columbia University IEOR-DRO seminar, December 2010. Stanford University Probability Seminar, May 2011.

Exchangeability and continuum limits of discrete random structures. ICM 2010, Hyderabad, August 2010.

Connected spatial random networks. Newton Institute, April 2010.

Mixing Times and Hitting Times. Lecture in AMS short course, San Francisco, January 2010.

Spatial random networks . Pacific Northwest Probability Seminar, U. Washington, October 2009.


Talks below the line are old school LaTeX slides, which tend to have missing material (hand-drawn figures or figures copied from other sources).


4 Lectures on local weak convergence from the Probability at Warwick Young Researchers Workshop, July 20-24, 2009.

Spatial Random Networks. Stochastic Networks conference, Paris, June 2008.

Some broad questions about the Tree of Life. Newton Institute, Cambridge, December 2007.

When Knowing Early Matters: Gossip, Percolation and Nash Equilibria. ICTP, Trieste, July 2007.

Short length routes in low cost networks Talk by co-author Wilf Kendall, September 2007: much better than my talks! As is this poster presentation.

Spatial random Networks Various places, October 2006 - May 2007. Later version is above.

Flows through random networks. SPASWIN, Boston, April 2006.

Optimal flow through the disordered lattice Berkeley, February 2006.

Flows through random networks. INFORMS, Ottawa, July 2005.

Percolating paths through random points Oberwolfach, May '05.

A Tractable Complex Network Model Cornell, U.C.L.A, March 2005.

Local weak convergence of random networks: towards the cavity method MSRI Berkeley, March 2005.

Constrained Ising models and speculative application to sensor networks Confererence in honor of Persi Diaconis, UC San Diego, January 2005.

Workshop Introduction: Models of real-world networks MSRI, Berkeley, January '05.

Random graphs, the multiplicative coalescent and percolation of tree-averages Newton Institute, December '03.

Mean-field combinatorial optimization, fixed point equations, and local weak convergence Berkeley, November '02; UCSB, December '02; Stanford, February '03, Microsoft Research, February '03.

Maximum partial matchings on random trees; an illustration of the local weak convergence methodology. Colloque Informatique et Mathematiques, Versailles, September '02.

A survey of max-type recursive distributional equations. Probability Symposium, Banff, July '02.

How to Combine Fast Heuristic Markov Chain Monte Carlo with Slow Exact Sampling SPA conference, Cambridge, July '01.

Mathematical Probability: some topics we understand, some we don't The Mordell Lecture, University of Cambridge, May '01.

Random graphs and complex networks. Berkeley (March '01).

The zeta(2) limit in the random assignment problem. Berkeley (October '00), Stanford (December '00).

The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results Berkeley (March '00), Stanford (February '00), Madison (February '02).


Slides from lectures given in Berkeley in Spring 2000, and at the Fourth Brazilian School of Probability, Mambucaba, August 2000.

Lecture 1 Coalescence in physical science; the basic deterministic and stochastic models.

Lecture 2 The gelation phase transition and the multiplicative case.

Lecture 3 Overview of stochastic coalescence results; the additive case.

Lecture 4 The hashing (parking) model: recent work of Chassaing-Louchard and Bertoin on the additive case.


Just for a historical record, I was an early adopter of SliTeX: here is

my 1990 talk that was written up as The Continuum Random Tree II

without the pictures that were hand-drawn ......

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