Dr. Alexander Zass

ehemaliger Mitarbeiter

Kontakt


I am a PhD student at the University of Potsdam, under the supervision of  Prof. Dr. Sylvie Roelly  and  Prof. Dr. Gilles Blanchard (now at Paris Orsay).

I am a fellow of the Graduate Program SFB 1294, Project A05.

I completed my Master's degree in Padua at Università degli Studi di Padova, with a thesis on “Collective motion of living organisms: the Vicsek model”, and my advisor was Prof. Paolo Dai Pra.

Personal webpage

 

Publications and preprints

2021 | Gibbs point processes on path space: existence, cluster expansion and uniqueness | Alexander ZassZeitschrift: SubmittedLink zum Preprint

Gibbs point processes on path space: existence, cluster expansion and uniqueness

Autoren: Alexander Zass (2021)

We study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to ℝd, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.

Zeitschrift:
Submitted

2020 | An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions | Pierre Houdebert, Alexander ZassZeitschrift: Journal of Applied Probability (June 2022)Link zur Publikation , Link zum Preprint

An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions

Autoren: Pierre Houdebert, Alexander Zass (2020)

We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity z and inverse temperature β. The technique used relies on applying to the continuous setting the classical Dobrushin criterion. We also present a comparison to the two other uniqueness methods of cluster expansion and disagreement percolation, which can also be applied for this type of interactions.

Zeitschrift:
Journal of Applied Probability (June 2022)

2020 | A Gibbs point process of diffusions: existence and uniqueness | Alexander ZassZeitschrift: Lectures in Pure and Applied MathematicsVerlag: Potsdam University PressBuchtitel: Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical PhysicsSeiten: 13-22Band: 6Link zur Publikation , Link zum Preprint

A Gibbs point process of diffusions: existence and uniqueness

Autoren: Alexander Zass (2020)

In this work we consider a system of infinitely many interacting diffusions as a marked Gibbs point process. With this perspective, we show, for a large class of stable and regular interactions, existence and (conjecture) uniqueness of an infinite-volume Gibbs process. In order to prove existence we use the specific entropy as a tightness tool. For the uniqueness problem, we use cluster expansion to prove a Ruelle bound, and conjecture how this would lead to the uniqueness of the Gibbs process as solution of the Kirkwood-Salsburg equation.

Zeitschrift:
Lectures in Pure and Applied Mathematics
Verlag:
Potsdam University Press
Buchtitel:
Proceedings of the XI international conference Stochastic and Analytic Methods in Mathematical Physics
Seiten:
13-22
Band:
6

2020 | Marked Gibbs point processes with unbounded interaction: an existence result | Sylvie Roelly, Alexander ZassZeitschrift: Journal of Statistical PhysicsSeiten: 972–996Band: 179Link zur Publikation , Link zum Preprint

Marked Gibbs point processes with unbounded interaction: an existence result

Autoren: Sylvie Roelly, Alexander Zass (2020)

We construct marked Gibbs point processes in ℝd under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an as finite but random range. Secondly, the random marks - attached to the locations in ℝd - belong to a general normed space S. They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.

 

Zeitschrift:
Journal of Statistical Physics
Seiten:
972–996
Band:
179

Other scientific works

- PhD Thesis (supervised by Prof. Sylvie Rœlly and Prof. Gilles Blanchard): A multifaceted study of marked Gibbs point processes

- Master's thesis (supervised by Prof. Paolo Dai Pra): Collective motion of living organisms: the Vicsek model

- Bachelor's thesis (supervised by Prof. Carlo Mariconda): Nonsmooth analysis and the maximum principle in control theory

Co-organisation of international Workshops

In the framework of the international projects of the Chair of Probability, I co-organised the following: