Jan Swart - Presentations

Three talks at Focused workshop on the Brownian web, the Brownian net and their geometry, Budapest, March 31 - April 4, 2024:

• The Brownian web and net.
• Topologies on sets of paths.
• Augmented Brownian webs as the scaling limit of non-simple coalescing random walks.

A numerical search for intertwining relations. Talk in the workshop Intertwining between Probability, Analysis and Statistical Physics at NUS, Singapore, August 13, 2024. This talk is partially based on the following research note and accompanying collection of scripts.

A min-max random game on a graph that is not a tree. Talk in the Probability Seminar at NUS, Singapore, July 31, 2024.

Here is a very similar talk given at the Applied Probability Workshop, Prague, June 25, 2024. I gave a short version of this talk at the German Probability and Statistics Days in Dresden, March 11-14, 2025.

The Brownian web and net. Talk at the conference Probability and Analysis, Będlewo, April 22-26, 2024.

Universality of the Brownian net. Talk at the workshop Eurandom 25 Years!, Eindhoven, April 15-17, 2024.

Monotone interacting particle systems. Minicourse at the workshop Dynamic spatial random systems, at the Weierstrass Institute, Berlin, January 29-31, 2024.

1. Interacting particle systems and the backward process
2. Monotone duality
3. The mean-field limit
4. The cooperative contact process
5. Toom contours

Pathwise duality for monotone interacting particle systems. Talk on the Workshop on Noise Sensitivity (iid and beyond) at the Rényi Institute and the Erdős Center in Budapest, January 8-12, 2024.

Weaves, webs and flows. Talk in the Probability seminar at Durham, 24.11.2023, 13:05-13:55. (This is a radically updated version of the talk of the same name listed below.)

Peierls bounds for Toom contours Talk in the Sheffield probability seminar, November 22, 2023. This is an updated version of the talk I gave at the Oberwolfach workshop Population Dynamics and Statistical Physics in Synergy (6-12.3 2022). The latter is identical to the talk I gave in the online Probability Seminar in Bristol, 22.4.2022.)

Pathwise dualities of interacting particle systems. Minicourse at the Rencontres de Probabilités 2023, Rouen September 21-22, 2023.

1. Interacting particle systems and the backward process
2. Monoid duality
3. Monotone duality

The Brownian web and net. Lecture notes for my course at the spring school Probabilistic methods in population biology, Darmstadt, March 27-31, 2023.

On Skorohod's topologies. Talk in the Seminar on stochastic evolution equations, UTIA, 20.2.2023, 15:40-17:10.

Pathwise duality for monotone Markov processes. Talk at the workshop Recent Developments in Stochastic Duality, Eindhoven, Thu 15.12.2022, 11:00-11:45.

The Brownian net, the branching-coalescing point set, and the one-dimensional 1-facilitated Frederickson-Anderson model. Lecture notes for a series of four lectures at the workshop Markov Chains with Kinetic Constraints and Applications Banff, July 3-8, 2022. Here are the notes for my blackboard talks. Here are videos of the first talk, second talk, third talk, and fourth talk.

Weaves, webs and flows I and II. Two talks of a series of three, given together with Nic Freeman at the workshop Population Genetics, Interacting Particle Systems and Stochastic Flows: a duality perspective Bonn, June 20-24, 2022. Here is the recorded talk.

O Brownově pavučině a síti. Přednáška na Konferenci českých matematiků VŠB-TU Ostrava, 4-6.4 2022.

Frozen percolation on the binary tree is nonendogenous. Blog on YoungStatS, 25.11.2021.

Frozen percolation on the binary tree Talk given at the German Probability & Statistics Days Mannheim (27.9 - 1.10 2021).

Frozen percolation on the binary tree Talk given at the workshop Stochastic Analysis and Its Applications XVI, Prague, January 3, 2020, at the workshop Geographic spaces for evolution: from lattices to graphs to continuum, Erlangen, December 13, 2019, and at the Seminar Extremal Graph Theory, ÚI AV ČR, Prague, October 25, 2019, 10:00-11:00. Here is a similar talk given at the Applied Probability Meeting, Nice, Sep 26-27, 2019.

Recursive tree processes and the mean-field limit of stochastic flows Talk given in the webinar Theory of Markov Semigroups and Schrödinger Operators at Wrocław University of Science and Technology, October 9, 2020 10:15–11:15.

The talk above is very similar to my talk given in the Stochastics seminar at the Institute of Mathematics of the TU Budapest - BME, January 30, 2020, my talk given at the Biomathematics Seminar, University of Bielefeld, July 4, 2019, my talk given at the Vienna Probability Seminar, January 29, 2019, my talk at the workshop Workshop STOCHASTIKA 2019 Kohútka, Nový Hrozenkov, February 7, 2019, my talk at the workshop Stochastic Processes and Random Trees October 11th, 2018, Dresden, my talk at the Rhein-Main Kolloquium Statistik Mainz, July 6, 2018, my talk at the workshop Stochastic Analysis and Its Applications XIV, KPMS MFF UK, Karlín, Prague, January 5th, 2018, and my talk at at the Seminar Extremal Graph Theory, ÚI AV ČR, Prague, December 8, 2017, 10:00-11:00.

Strong R-positivity. Three lectures given in the Seminar on stochastic evolution equations, Prague, February-April 2019.

Interface tightness. Talk given at the workshop Population Dynamics and Statistical Physics in Synergy II, Pisa, April 1-3, 2019.

Interface tightness. Talk given at the workshop Spatial Population Models: From configurations to genealogies and back, Erlangen, March 25-27, 2019.

Here is a very similar talk given at the workshop Stochastic Analysis and Its Applications XV Prague, January 4th, 2019.

Sharpness of the phase transition for the contact process. Talk at the 40th Conference on Stochastic Processes and their Applications – SPA 2018., Gothenburg, Sweden, 11-15th of June 2018.

Here is a very similar talk I gave at the workshop Guided Tour: Random Media on the occasion of the 60th birthday of Frank den Hollander.

A Fresh Look at R-positivity. Talk at the seminar Stochastik-Tage 2018 Freiburg, February 28, 11:10-11:30.

A longer version of more or less the same talk is: Necessary and sufficient conditions for strong R-positivity. Talk at the seminar BESEDA of the Katedra pravděpodobnosti a matematické statistiky MFF UK, Prague, November 29, 2017, 15:40-16:40.

The algebraic approach to duality (August 4, 2017). A learning session on the work of Giardinà, Redig and others presented together with Anja Sturm and Florian Völlering during the program Genealogies of Interacting Particle Systems, Institute for Mathematical Sciences, Singapore, 17 Jul - 18 Aug 2017.

Cooperative branching and pathwise duality for monotone systems. Talk in the AG Stochastik und Dynamische Systeme, Department Mathematik, Erlangen, April 27, 2017, 14:14-16:00.

The Brownian net. Talk on the workshop Stochastika 2017, Kohútka, February 5-10, 2017.

The Stigler-Luckock model with market makers. Talk together with Vít Peržina on the workshop Stochastic analysis and its applications XIII, Prague, January 7, 2017.

Self-organised criticality on the stock market. The 2016 Applied Probability Trust Lecture, Sheffield Probability Day, September 21st, 2016, at the School of Mathematics and Statistics.

The Stigler-Luckock model for the evolution of an order book. Talk on the World Congress in Probability and Statistics., July 11-15, 2016, Toronto.

A simple proof of exponential decay of subcritical contact processes. Talk in the Seminar on stochastic evolution equations, UTIA, April 11 and 18, 2016.

Cooperative branching and pathwise duality for monotone systems. Talk in the Probability and Statistics Seminar, University of Bristol, 26 February 2016.

An intertwining-based renormalization argument for hierarchical contact processes. Talk on the Alan Sokal's 60th birthday Workshop, November 24th, 2015, Paris.

Rank-based Markov chains, self-organized criticality, and order book dynamics. Talk in the Seminar at the Probability Laboratory, February 29th 2016, Bath.

Here are a shortened version of the above talk given at the Stochastik-Tage Bochum 2016 and an earlier version given at the Kolloquium Stochastik, June 17th 2015, TU Berlin. Teď i s českým překladem. This was again a slightly updated version of the same talk as given on the workshop Workshop on Stochastic Processes in Random Media, May 4-15th, 2015, Singapore.

Self-organized criticality on the stock market . Talk on the workshop Stochastic analysis and its applications XI, January 5th, 2015, Prague.

The Brownian net. Talk in the AG Stochastik und Dynamische Systeme, November 21th, 2014, Erlangen.

Some dualities for a class of one-dimensional cancellative systems. Talk on the Workshop Duality, November 7th, 2014, Berlin.

Interacting Particle Systems with Applications in Finance, Verona, Oct 20, 22, and 23, 2014:

0. Preliminaries
1. Introduction
2. Mean-Field Analysis
3. Construction of Infinite Systems and Uniqueness of the Invariant Law
4. Monotonicity
5. Duality
6. The Contact Process

On rebellious voter models Talk on the Workshop Population Dynamics and Statistical Physics in Synergy, August 29th, 2014, Eindhoven.

Cooperative branching Talk on the Workshop Genealogies of population models with competition, June 27th, 2014, Essen.

Random 3-colourings and a phase transition for the 3-state Potts antiferromagnet on a class of planar lattices. Talk on the Workshop Combinatorics and Statistical Mechanics, April 7-11, 2014, as part of the 2013-14 Warwick EPSRC Symposium on Statistical Mechanics.

On rebellious voter models. Talk on the 11th German Probability and Statistics Days, March 6th, 2014, Ulm.

Subcritical contact processes seen from a typical infected site. Talk on the workshop From interacting particle systems to population genetics, February 27th, 2014, Erlangen.

Duality and Intertwining of Markov Chains. Two lectures, plus a problem session, presented at the ALEA in Europe School October 21-25 at CIRM, in Luminy (Marseille).

On rebellious voter models. Talk in the Probability Seminar of Maths Dept. of the the NUS, July 11th, 2013, Singapore. Here is almost the same talk given in the Seminar on Probability Theory, June 18th, 2013, Vienna.

Systems of branching, annihilating, and coalescing particles. Talk in the Workshop Stochastic Analysis and Applications IX, January 3-4th, 2013, Prague.

Antiferromagnetic Potts models and random colorings of planar graphs Slides of my talk at the Stochastik-Tage Mainz, 6-9 March 2012. Here is an updated version of this talk given at the Seminar on stochastic evolution equations in Prague.

Stochastic Order Book Dynamics Talk by Jana Plačková and me, based on her master thesis, in the Workshop Stochastic Analysis and Applications VIII, January 6-7th, 2012, Prague.

The contact process seen from a typical infected site Slides of my talk at the Frankfurt Seminar on Random Discrete Structures, 8-9 September 2011.

Stochastic flows in the Brownian web and net Slides of my talk at the Workshop on Branching Processes and Coalescent processes, Beijing Normal University, April 18-22, 2011..

Intertwining of Markov processes Talk in the AG Stochastik und Dynamische Systeme, Erlangen, January 13th, 14:15-16:00. I presented a shorter version of this talk at the 7th Workshop on Stochastic analysis and its applications, Prague, Jan 3-4, 2011.

Stochastic flows in the Brownian web and net Slides of my talk at the Stochastic Analysis Seminar in Oxford.

On rebellious voter models Slides of my talk at the IMS 2010 in Gothenburg..

Intertwining of Markov processes and the contact process on the hierarchical group Slides of my talk at the Rhein-Main Kolloquium Stochastik.

Stochastic flows in the Brownian web and net Slides of my talk at the SPA Berlin 2009.

O Brownove pavucine a site ("The Brownian web and net") Talk for a general audience on the occasion of UTIA's 50th anniversary.

Two posters for the Workshop Interacting Particle Systems and Percolation Paris, 27-31 October 2008

Survival of contact processes on the hierarchical group. Poster, A4 version of the poster.

The contact process seen from a typical infected site. Poster, A4 version of the poster.