Stochastik und ihre Anwendungen

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  7. Probability Colloquium Augsburg-Munich

Probability Colloquium Augsburg-Munich

Next event in Munich:

 

Monday, 16 December 2024 at LMU Munich

Department of Mathematics, Room B 349, Theresienstr. 39, 80333 München
 

Speakers:

 

Schedule:

 

14:30               Welcome

15:00 - 16:00   Talk Alexander Glazman

16:00               Coffee break

16:30 - 17:30   Talk Felix Joos

 

Titles and abstracts:

 

Alexander Glazman: Phase diagram of the loop O(n) model

 

Phase transitions are natural phenomena in which a small change in an external parameter, like temperature or pressure, causes a dramatic change in the qualitative structure of the object. To study this, many scientists (such as Nobel laureates Pauling and Flory) proposed the abstract framework of lattice models. The focus of this talk is on the loop O(n) model on the hexagonal lattice. Among its particular cases are percolation, Ising model, self-avoiding walk, dimers, integer-valued Lipschitz functions, proper 4-colourings and others. The loop O(n) model has attracted a lot of attention due to its rich phase diagram that includes a large region of parameters with an expected conformally invariant scaling limit. The model is difficult to study due to the lack of monotonicity with respect to parameters: each point of the phase diagram should be treated separately. In particular, existence of macroscopic loops has been established only recently in several sparse regions of parameters. I will present a unifying approach that applies to all n between 1 and 2. Main tools: novel graphical representation, Benjamini—Schramm limit, XOR argument (aka arXiv:2001.11977) and a new bound on a percolation threshold (due to Harel and Zelesko). This is joint work with Matan Harel (Northeastern).

 

 

 

Felix Joos: The hypergraph removal process

 

Fix some graph or uniform hypergraph F and then consider the following simple process:
start with a large complete (hyper)graph Kn on n vertices and iteratively remove (the edge set of) copies of F as long as possible; each selection is made uniformly among all present copies of F at that time. This process is known as the F-removal process. The determination of the termination time (how many edges are left when the process terminates) is the key question regarding this process. This question has proven to be highly challenging. Bohman, Frieze and Lubetzky famously proved in 2015 that the triangle-removal process (F is a triangle) typically terminates with n3/2+o(1) edges. For no other (hyper)graph F has the termination of the F-removal process been established. We determine when the F-removal process ends for all "sensible" choices of F; this includes cliques, for which a major folklore conjecture in this area predicts the termination time.
This is joint work with Marcus Kühn.

 

Next event in Augsburg:

 

Friday, 24 January 2025 at Augsburg University

Institute of Mathematics, room 2004 (L1), Universitätsstraße 14, 86159 Augsburg

 

Speakers:

 

Schedule:

 

14:30               Welcome

15:00 - 16:00   Talk Lorenzo Taggi

16:00               Coffee break

16:30 - 17:30   Talk Benedikt Jahnel

 

Titles and abstracts:

Lorenzo Taggi: t.b.a.

 

 

Benedikt Jahnel: Dynamical Gibbs variational principles for irreversible interacting particle systems with applications to attractor properties
 
In this talk, we consider irreversible translation-invariant interacting particle systems on the d-dimensional hypercubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove, that zero relative entropy loss of a translation-invariant measure implies, that the measure is Gibbs with respect to the same specification as the time-stationary Gibbs measure. As an application, we obtain the attractor property for irreversible interacting particle systems, which says that any weak limit point of any trajectory of translation-invariant measures is a Gibbs measure with respect to the same specification as the time-stationary measure. This extends previously known results to fairly general irreversible interacting particle systems and joined work with Jonas Köppl. 
 
 
 

Organizers

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