AP Seminar

The 2025–26 Warwick Statistics Applied Probability Seminar will be held on Fridays 11am–12pm in MB0.08. We will join afterwards for coffee/lunch in the Statistics Common Room at 12pm. Everyone is welcome. Please email if you would like to speak or invite a speaker.

(Warwick also has a Probability Seminar on Wednesdays 4–5pm in B3.02.)

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Term 1

*** Special out-of-term seminar. Note unusual time and place. ***
Tues, Sep 9 @ MS.05, 4–5pm
Speaker: Simon Harris (Auckland, Stats)
Title: Genealogies of samples from stochastic population models
Abstract: Consider some population evolving stochastically in time. Conditional on the population surviving until some large time $T$ , take a sample of individuals from those alive. What does the ancestral tree drawn out by this sample look like? Some special cases were known, e.g. Durrett (1978), Athreya (2012), O’Connell (1995), but we will discuss some more recent advances when sampling from Bienyame-Galton-Watson (BGW) branching processes conditioned to survive. In near-critical or in critical varying environment BGW settings with finite offspring variances, the same universal limiting sample genealogy always appears up to some deterministic time change which only depends on the mean and variance of the offspring distributions. This genealogical tree has the same binary tree topology as the classical Kingman coalescent, but where the coalescent (or split) times are quite different due to stochastic population size effects, with a representation as a mixture of independent identically distributed times. In contrast, in critical infinite variance offspring settings, we find that more complex universal limiting sample genealogies emerge that exhibit multiple-mergers, these being driven by rare but massive birth events within the underlying population e.g. `superspreaders’ in an epidemic. Our key tool for proofs is a change of measure technique involving $k$ distinguished particles, also known as spines. Some ongoing work, open problems, and potential downstream applications will also be mentioned. This talk is based on collaborative works with Juan Carlos Pardo (CIMAT), Samuel Johnston (Kings College London) in Annals of Probability (2024), with Sandra Palau (UNAM), J. C. Pardo in Annals of Applied Probability (2024), and with Matt Roberts (Bath), S. Johnston in Annals of Applied Probability (2020). I would also like to acknowledge the support of the New Zealand Royal Society Te Apārangi Marsden fund.
Fri, Oct 10 @ MB0.08, 11am–12pm
Speaker: Oleg Zaboronski (Warwick, Maths)
Title: On the structure of coalescing Ito's diffusions
Abstract: We consider a system of coalescing Ito's diffusion on the real line starting in the maximal entrance law. The corresponding stochastic process generalises both the celebrated Arratia flow as well as the Arratia flow with drift. We show that the one-dimensional distributions are a Pfaffian point process and characterise its kernel as the unique solution to a two-dimensional parabolic equation in half-plane. We apply the Pfaffian structure to the study of the invariant measures for the process. In particular we find that the invariant measure for the unit-variance diffusions with the linear drift $V(x)=-x$ which pushes particles towards the origin is given by the the Pfaffian point process corresponding to the law of real eigenvalues in the real Ginibre ensemble of random matrices. We also study the space of invariant measure for the unit diffusion and the family of algebraic drifts $V(x)=-\mbox{sign}(x) |x|^\alpha$ , $\alpha \in [0,1)$ . We find that at $\alpha=1/3$ the process undergoes a phase transition from the unique (one-particle) steady state to a multi-state phase. Work in progress in collaboration with Roger Tribe, Mykola Vovchansky and Andrey Dorogovtsev.
Fri, Oct 17 @ MB0.08, 11am–12pm
Speaker: Isabella Gonçalves de Alvarenga (Warwick, Stats)
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Fri, Oct 24 @ MB0.08, 11am–12pm
Speaker: Tomasz Przybyłowski (Oxford, Maths)
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Fri, Oct 31 @ MB0.08, 11am–12pm
Speaker: John Fernley (Warwick, Stats)
Title: The grass-bushes-trees process on a scale-free network
Abstract: The grass-bushes-trees process is a two-type contact process in which one type (the trees),of infection parameter $lambda_1$ , can invade the other type (the bushes) of infection parameter $lambda_2$ . We look to show which graph parameters lead to the possibility of coexistence versus the necessity of competitive displacement, i.e. joint metastability or fast extinction of the bushes. Work in progress with Daniel Valesin.
Fri, Nov 7 @ MB0.08, 11am–12pm
Speaker: Peter Koepernik (Oxford, Stats)
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Fri, Nov 14 @ MB0.08, 11am–12pm
Speaker: Andreas Kyprianou (Warwick, Stats)
Title: The Brownian marble
Abstract: Fundamentally motivated by the two opposing phenomena of fragmentation and coalescence, we introduce a new stochastic object which is both a process and a geometry. The Brownian marble is built from coalescing Brownian motions on the real line, with further coalescing Brownian motions introduced through time in the gaps between yet to coalesce Brownian paths. The instantaneous rate at which we introduce more Brownian paths is given by $\lambda/g^2$ where $g$ is the gap between two adjacent existing Brownian paths. We show that the process “comes down from infinity” when $0<\lambda<6$ and the resulting space-time graph of the process is a strict subset of the Brownian Web on ${\mathbb R} \times [0,\infty)$ . When $\lambda\geq 6$ , the resulting process “does not come down from infinity” and the resulting range of the process agrees with the Brownian Web.
Fri, Nov 21 @ MB0.08, 11am–12pm
Speaker: Gareth Roberts (Warwick, Stats)
Title: Ballistic and diffusive lifted MCMC, with application to parallel tempering
Abstract: In this talk I will review the popular “lifting” mechanism for producing non-reversible Markov chain Monte Carlo such as non-reversible Metropolis-Hastings and piecewise-deterministic Markov processes. These methods aim to have better mixing by providing momentum to break down random walk behaviour of algorithms. The presentation will investigate how these behave in a collection of stylised high-dimensional examples showing that the non-reversibility can often be washed out by the problem complexity so that the algorithm behaves asymptotically in a reversible way. On the other hand lifted algorithms still retain a small efficiency advantage over their reversible counterparts. Furthermore, we will show that some carefully constructed higher-order lifted Metropolis-Hastings algorithms can retain some aspects of ballistic behaviour, even in the high-dimensional limit setting.
Fri, Nov 28 @ MB0.08, 11am–12pm
Speaker: Oleg Pikhurko (Warwick, Maths)
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Fri, Dec 5 @ MB0.08, 11am–12pm
Speaker: Ian Melbourne (Warwick, Maths)
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Fri, Dec 12 @ MB0.08, 11am–12pm
Speaker: Vedran Sohinger (Warwick, Maths)
Title: The large-mass limit of interacting Bose gases in the continuum
Abstract: We consider Bose gases in thermal equilibrium and show convergence of the grand-canonical Gibbs state to the corresponding large-mass (classical particle) limit. This limit corresponds to a classical theory of point particles with two-body interactions. Our analysis is carried out in the continuum. The analogous result on the lattice was previously shown by Fröhlich, Knowles, Schlein, and Sohinger. A challenge in the continuum is the unboundedness of the heat kernel, which requires us to suitably tune the chemical potential. The main tool of our analysis is the random loop representation of the interactions due to Ginibre. In this framework, we can obtain quantitative estimates on convergence for the partition function and reduced p-particle density matrices. In the finite volume, we are able to work with stable interaction potentials. This is a joint work with Spyros Garouniatis (Brandeis University) and Grega Saksida (University of Warwick).

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Term 2

Fri, Jan 16 @ MB0.08, 11am–12pm
Speaker: Karen Habermann (Warwick, Stats)
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Fri, Jan 23 @ MB0.08, 11am–12pm
Speaker: Charilaos Efthymiou (Warwick, CS)
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Fri, Jan 30 @ MB0.08, 11am–12pm
Speaker: Grega Saksida (Warwick, Maths)
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Fri, Feb 6 @ MB0.08, 11am–12pm
Speaker: Emma Horton (Warwick, Stats)
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Fri, Feb 13 @ MB0.08, 11am–12pm
Speaker: Georgii Zakharov (Oxford, Maths)
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Fri, Feb 20 @ MB0.08, 11am–12pm
Speaker: Seth Hardy (Warwick, Maths)
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Fri, Feb 27 @ MB0.08, 11am–12pm
Speaker: Thomas Hughes (Bath, Maths)
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Fri, Mar 6 @ MB0.08, 11am–12pm
Speaker: Pablo Ramses Alonso Martin (Warwick, Stats)
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Fri, Mar 13 @ MB0.08, 11am–12pm
Speaker: Wilfrid Kendall (Warwick, Stats)
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Fri, Mar 20 @ MB0.08, 11am–12pm
Speaker: Debsoumya Chakraborti (Warwick, Maths)
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Term 3

Fri, May 1 @ MB0.08, 11am–12pm
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Fri, May 8 @ MB0.08, 11am–12pm
Speaker: Jiayao Shao (Warwick, Stats)
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Fri, May 15 @ MB0.08, 11am–12pm
Speaker: Adam Johansen (Warwick, Stats)
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Fri, May 22 @ MB0.08, 11am–12pm
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Fri, May 29 @ MB0.08, 11am–12pm
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Fri, Jun 5 @ MB0.08, 11am–12pm
Speaker: Thomas Morrish (Warwick, Stats)
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Fri, Jun 12 @ MB0.08, 11am–12pm
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Fri, Jun 19 @ MB0.08, 11am–12pm
Speaker: Janique Krasnowska (Warwick, Stats)
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Fri, Jun 26 @ MB0.08, 11am–12pm
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Fri, Jul 3 @ MB0.08, 11am–12pm
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