*The Science Park Informal Probability (SPIP) *meetings is a seminar for all people interested in probability theoretical topics and related fields. The SPIP was created some years ago by a group of PhD candidates from the KdVI and the CWI, both institutes are located at the science park, to have a joint seminar that takes place on a regularly basis and where one can talk in an informal way about all subjects related to stochastics, statistics or machine learning. We want to keep this spirit of the seminar and invite all fellow stochastic enthusiasts to join us in our seminar on the science park.

A reminder will be sent out for each talk. To subscribe to receive these reminders please send an email with the subject 'subscribe' to spip.meetings@gmail.com.

## Upcoming

## Previous

Date: Tuesday, 16/11, 14:00-15:00

Speaker: **Peter Bolhuis** (from UvA) Title: Sampling and reweighting of unbiased molecular dynamics trajectories Abstract: Atomistic models are extremely powerful in the natural sciences, with applications in physics, chemistry, materials science and biology. Combining such physics-based atomistic models with molecular or stochastic) dynamics simulations in principle provides predictions of the dynamics of all kinds of processes on an atomistic level that are complementary to experiment. Applications range from chemical reactions, to phase transitions, to biomolecular conformational changes, signaling and regulation. However, in practice, molecular dynamics is far from fulfilling this promise due to exceedingly long simulation times involved, also known as the rare event problem. One can overcome this problem by focusing on the dynamical trajectories undergoing the rare event process. By constructing a probability distribution for the process at hand, and harvesting dynamical trajectories by importance sampling one can access the relevant time scales without any further approximations, and get insight into e.g. the mechanism, or the mean first passage times. The resulting ensembles of trajectories can also be scrutinized for useful insight based on commitment probability distribution, aka the committor. Over the past decade such path sampling algorithms have been developed and applied to many systems, of which I will highlight a few. Finally, recently we introduced a novel method to incorporate experimental dynamical observables as constraints in the obtained path ensembles using the Maximum Caliber framework. I will discuss the fundamentals of this approach, show how it can be used to reweight the trajectoriy probabilities to correct for systematic errors in the underlying models.

Date: Tuesday, 09/11 - 16:00-17:00

Speaker: **Mauricio del Razo Sarmina** (from UvA) Title: A probabilistic framework for reaction-diffusion dynamics using classical Fock space representations Location: CWI, Room 102 Abstract: The modeling and simulation of stochastic reaction-diffusion processes is a topic of steady interest that is approached with a wide range of methods. For the highly resolved level of particle-based dynamics there exist comprehensive numerical simulation schemes, while the corresponding mathematical formalization is not yet fully developed. The aim of this work is to derive the probabilistic evolution equation for chemical reaction kinetics that is coupled to the spatial diffusion of individual particles, as well as to develop a framework for systematically formulating, analyzing, and coarse-graining their stochastic dynamics. To account for the non-conserved and unbounded particle number of this type of open systems, we employ a classical analogue of the quantum mechanical Fock space that contains the symmetrized probability densities of the many-particle configurations in space. Following field-theoretical ideas of second quantization, we introduce creation and annihilation operators that act on single-particle states and that provide natural representations of symmetrized probability densities as well as of reaction and diffusion operators. The resulting evolution equation, termed chemical diffusion master equation (CDME), serves as the foundation to derive more coarse-grained descriptions of reaction-diffusion dynamics. Paper link: https://arxiv.org/abs/2109.13616 Date: Wednesday, 06/10, 16:00-17:00 Speaker: **Emma Horton** ( Chargé de Recherche at Bordeaux university, Guest of Michel Mandjes at the KdVI) Title: Asymptotic behaviour of branching piecewise deterministic Markov processes Abstract: Branching piecewise deterministic Markov processes (PDMPs) can be used to model a range of real-world processes such as neutron transport, cell division and protein polymerisation. Thus, it is crucial to understand their long-term behaviour. In this talk, I will introduce a general class of branching PDMPs in a bounded domain and show that under mild assumptions, a Perron Frobenius type result holds for the average of the process. That is, I will prove the existence of the leading eigenvalue and corresponding eigenfunctions of the linear semigroup, and show that they characterise the asymptotic macroscopic behaviour of the system. I will also discuss a new simulation technique based on population control methods that can be used to estimate these quantities.

Date: Thursday, 23/09, 15:00-16:00

Speaker: **Martin Friesen** (from Dublin City University) Title: *Ergodicity of affine processes in finite and infinite dimensions* Chair/wo/man: Sven

Abstract: A Markov process whose log-characteristic function is affine in the initial state of the process is called affine process. A remarkable feature is that its log-characteristic function can actually be expressed in terms of a solution to a generalized Riccati equation with a characteristic exponent of a Levy process as the right-hand side of the equation. Such property is satisfied by several interesting classes of Markov processes such as Ornstein-Uhlenbeck processes, continuous-state branching processes with immigration, and Dawson-Watanabe superprocesses. In this talk, we study limiting distributions, invariant measures, and ergodicity for affine processes on finite and infinite-dimensional state spaces. Our methods are either based on the study of the corresponding generalized Riccati equation or on a pathwise representation of affine processes in terms of solutions to stochastic differential equations. Extensions of the results to affine Volterra processes are also discussed at the end of the talk.