# Applied Probability Seminars

This is an informal seminar to give academic staff, visitors, graduate students, etc., based or hosted in Warwick (any department), the opportunity to know more about each other’s research on topics of probability and its uses in related areas such as mathematical statistics, statistical physics, computer sciences, analysis, et cetera.

PhD students and postdocs are particularly encouraged to contribute, as well as any external speaker from other departments or universities that you would like to invite. Please contact Daniel Valesin (daniel.valesin<at>warwick.ac.uk) if you wish to give a talk or if you have a name of speaker to suggest.

Below is a provisional schedule of the upcoming talks. Given the informal nature of the seminar, last minute changes may happen. Please join the Applied probability Seminar Teams channel to receive up to date information.

###### Academic Year 2023-24, Term 1

Venue: MB0.08 (unless otherwise stated) or Online (Teams link will be provided in the Teams channel)

Time: 11:00 (unless otherwise stated) - followed by lunch in the Common Room.

**29 September 2023 (Welcome Week)**

**Venue is exceptionally MB2.24, time is exceptionally 14:00**

Speaker: **Abdelatif Bencherif-Madani **(Université Sétif 1 Ferhat Abbas)

**Title:** An entropic limit theorem for the boundary local time of a diffusion

**Abstract: **Let X be a symmetric diffusion reflecting in a $C^3$-bounded domain $D$ in the Euclidean space of dimension $n$, $n>=1$. Assume that the diffusion matrix is of class $C^2$, bounded and non-degenerate. For $t>0$, and $k, n$ positive integers, let $N(n,t)$ be the number of dyadic intervals $I_{n,k}$ of length $2^{-n}$, $k>=0$, that contain a time $s=<t$ such that $X_s$ belongs to the boundary of $D$. For a suitable normalizing factor $H(t)$, we prove, extending the one dimensional case, that a.s. for all $t>0$ the entropy functional $N(n,t)/H(2^{-n})$ converges to the boundary local time $L_t$ as $n\rightarrow \infty$. Motivations of this study include boundary value problems in PDE theory, efficient Monte-Carlo simulation, and Finance.

**6 October 2023**

Speaker: **Emma Horton**

**Title:** tba

**Abstract: **tba

**13 October 2023**

Speaker: **Victor Rivero **(CIMAT)

**Title:** tba

**Abstract: **tba

**20 October 2023**

Speaker: **Andreas Kyprianou**

**Title:** tba

**Abstract: **tba

**27 October 2023**

Speaker: **Conrado da Costa **(Durham University)

**Title:** Passage times for partially homogeneous reflected Random Walks on the quadrant

**Abstract:** In this talk we consider a partially homogeneous random walk on the quadrant with zero drift at the interior. The goal of the talk is to explain how to obtain qualitative and quantitative knowledge on the passage time of the origin and its moments. The focus of the talk is on the adaptation of the classical methods to our set up and the heuristics on how to obtain those classifications from both a probabilistic and a geometrical perspective. This is a joint work with Mikhail Menshikov and Andrew Wade.

**3 November 2023**

Speaker: tba

**Title:** tba

**Abstract: **tba

**10 November 2023**

Speaker: **Andreas Koller**

**Title:** Scaling limit of gradient models on $\Z^d$ with non-convex energy

**Abstract: **Random fields of gradients are a class of model systems arising in the study of random interfaces, random geometry, field theory and elasticity theory. The models we consider are characterised by an imposed boundary tilt and the free energy (called surface tension in the context of random interface models) as a function of tilt. Of interest are, in particular, whether the surface tension is strictly convex and whether the large-scale behaviour of the model remains that of the massless free field (Gaussian universality class). Where the Hamiltonian (energy) of the system is determined by a strictly convex potential, good progress has been made on these questions over the last two decades. Open problems include the conjecture that, in any regime of the parameters such that the scaling limit is Gaussian, its covariance (diffusion) matrix should be given by the Hessian of surface tension as a function of tilt. For models with non-convex energy fewer results are known. I will survey some recent advances in this direction using renormalisation group arguments and describe our result confirming the conjectured behaviour of the scaling limit for a class of non-convex potentials in the regime of low temperatures and small tilt. This is based on joint work with Stefan Adams.

**17 November 2023**

Speaker: **Brett Kolesnik **(Oxford)

**Title:** tba

**Abstract: **tba

**24 November 2023**

Speaker: **Marta Dai Pra **(Humboldt Universität)

**Title:** tba

**Abstract: **tba

**1 December 2023**

Speaker: (tba)

**Title:** tba

**Abstract: **tba

**8 December 2023**

Speaker: **Konrad Anand **(Queen Mary University)

**Title:** tba

**Abstract: **tba