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Department of Statistics

Applied Probability Seminar (2025-26)

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. (There is also a Probability SeminarLink opens in a new window on Wednesdays 4–5pm in B3.02.)

For visiting speakers: see here for a view of the room. It is possible to give a chalkboard talk, but the board is small. Beamer talks tend to work better in this room.

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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 HarrisLink opens in a new window (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.

  • *** Special out-of-term seminar. Note unusual time and place. ***
    Wed, Sep 24 @ MS.05, 11am–12pm
    Speaker: Kirstin StrokorbLink opens in a new window (Bath, Maths)
    Title: Graphical models for infinite measures with applications to extremes
    Abstract: Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure\Lambdaon the punctured Euclidean space $\mathbb R^d\setminus \{0\}$ that explodes at the origin. The importance of such measures stems from their connection to infinitely divisible and max-infinitely divisible distributions, where they appear as Lévy measures and exponent measures, respectively. We characterize independence and conditional independence for\Lambdain various ways through kernels and factorization of a modified density, including a Hammersley-Clifford type theorem for undirected graphical models. As opposed to the classical conditional independence, our notion is intimately connected to the support of the measure \Lambda. Our general theory unifies and extends recent approaches to graphical modeling in the fields of extreme value analysis and Lévy processes. Our results for the corresponding undirected and directed graphical models lay the foundation for new statistical methodology in these areas. Joint work with Sebastian Engelke, Jevgenijs Ivanovs; accepted in Annals of Applied Probability. Preprint: arXiv:2211.15769.

  • (Week 1) Fri, Oct 10 @ MB0.08, 11am–12pm
    Speaker: Oleg ZaboronskiLink opens in a new window (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.

  • (Week 2) Fri, Oct 17 @ MB0.08, 11am–12pm
    Speaker: Isabella Gonçalves de AlvarengaLink opens in a new window (Warwick, Stats)
    Title: The rightmost particle of the contact process on random dynamical environments
    Abstract: The contact process with inherited sterility provides a probabilistic framework for studying population control strategies inspired by the Sterile Insect Technique. Unlike full sterilization, where treated males lose competitiveness, the inherited sterility method introduces only partial sterility that is passed on to descendants, allowing the suppressive effect to propagate across generations. To analyse this model, and to compare it with related dynamics, we also introduce the Spont process, another example of a contact process in a random dynamical environment. We will define the dynamics of both processes on the one-dimensional integer lattice. In both cases, our main result is a central limit theorem for the position of the rightmost occupied site. The two models pose distinct challenges — the Spont process lacks self-duality, while the inherited sterility model is non-attractive. Our approach combines a renewal-time construction with a careful analysis of active infection paths, leading to an embedded i.i.d. structure for the increments of the position of the rightmost occupied site.

  • (Week 3) Fri, Oct 24 @ MB0.08, 11am–12pm
    Speaker: Tomasz PrzybyłowskiLink opens in a new window (Oxford, Maths)
    Title: Finding the Origin of a Random Walk
    Abstract: Suppose you are given the trace of a symmetric random walk on the integer lattice up to the $n$-th step, but without any information about the lattice’s labels. Can you identify the starting point of the walk with probability bounded away from zero? Interestingly, the answer depends on the dimension of the lattice. What if you are given only the set of visited vertices? What about the entire (infinite) trace? I will discuss these phenomena and related problems. Based on joint work with Ritesh Goenka and Peter Keevash.

  • (Week 4) Fri, Oct 31 @ MB0.08, 11am–12pm
    Speaker: Peter KoepernikLink opens in a new window (Oxford, Stats)
    Title: From $1/\sqrt{n}$ to $1/n$: Accelerating SDE Simulation with Cubature Formulae
    Abstract: Monte Carlo sampling is the standard approach for estimating properties of solutions to stochastic differential equations (SDEs), but its error decays only as $1/\sqrt{n}$, requiring huge sample sizes. Lyons and Victoir (2004) proposed replacing independently sampled Brownian driving paths with "cubature formulae", deterministic weighted sets of paths that match Brownian "signature moments" up to some degree $D$. They prove that cubature formulae exist for arbitrary $D$, but explicit constructions are difficult and have only reached $D=7$, too small for practical use. We present an algorithm that efficiently and automatically constructs cubature formulae of arbitrary degree, reproducing $D=7$ in seconds and reaching $D=17$ within hours on modest hardware. In simulations across multiple SDEs, our cubature formulae achieve an error roughly of order $1/n$, orders of magnitude smaller than Monte Carlo with the same number of paths. Based on joint work with Thomas Coxon and James Foster.

  • (Week 5) Fri, Nov 7 @ MB0.08, 11am–12pm
    Speaker: John FernleyLink opens in a new window (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.

  • (Week 6) Fri, Nov 14 @ MB0.08, 11am–12pm
    Speaker: Andreas KyprianouLink opens in a new window (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.

  • (Week 7) Fri, Nov 21 @ MB0.08, 11am–12pm
    Speaker: Gareth RobertsLink opens in a new window (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.

  • (Week 8) Fri, Nov 28 @ MB0.08, 11am–12pm
    Speaker: Oleg PikhurkoLink opens in a new window (Warwick, Maths)
    Title: Randomness for ball covering of large-dimensional Euclidean spaces
    Abstract: We will discuss the power and limitations of using randomness for proving the existence of coverings of ${\mathbb R}^n$, for large $n$, by Euclidean unit balls with small density (which is, informally speaking, the number of balls that contain a `typical' point of ${\mathbb R}^n$). This talk will be based on joint work with Boris Bukh, Jun Gao, Xizhi Liu and Shumin Sun (arXiv:2508.06446Link opens in a new window and arXiv:2510.25685Link opens in a new window).

  • (Week 9) Fri, Dec 5 @ MB0.08, 11am–12pm
    Speaker: Ian MelbourneLink opens in a new window (Warwick, Maths)
    Title: Convergence to Levy processes for deterministic dynamical systems
    Abstract: I will survey results over the last 10 years on convergence to Levy processes for deterministic dynamical systems. Convergence to a Levy process often holds when the central limit theorem fails. The limiting process is superdiffusive (growing like (time)^a with a>1/2) and sample paths have dense sets of discontinuities. Classical treatments of convergence to Levy processes use Skorokhod topologies from 1956. In the 1990s, Whitt recognised that convergence may fail in such topologies, and that important information may be lost even when convergence holds. Accordingly, Whitt introduced "decorated" Skorokhod-type topologies. However, there was a lack of examples to illustrate how best to proceed. It turns out that dynamical systems provide a wealth of examples where decorated topologies are needed. Moreover, their analysis leads to the correct (we claim!) definition of decorated Skorokhod topology. The precise definitions are technical. Instead I'll provide examples and pictures to illustrate the theory. This is joint work with Chevyrev & Korepanov and with Freitas, Freitas & Todd.

  • (Week 10) Fri, Dec 12 @ MB0.08, 11am–12pm
    Speaker: Vedran SohingerLink opens in a new window (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

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Term 3

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