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Random Networks Workshop
The University of Sheffield Probability Group invites you to attend a one-day workshop on the broad topic of Random Networks.
This workshop is the forth in a series which aims to bring together academics interested in random networks regularly to hear about exciting advancements in the field. This workshop has run in 2022, 2024, 2025, and 2026.
Please see below for details of this workshop as well as information about how to register.
Programme
Programme
09:00 - 09:30, Registration (tea/coffee + Pastries, catered by PJ Taste.)
09:00 - 09:30, Registration (tea/coffee + Pastries, catered by PJ Taste.)
Details TBC
10:30 - 11:00, Refreshments (tea/coffee + biscuits, catered by PJ Taste.)
10:30 - 11:00, Refreshments (tea/coffee + biscuits, catered by PJ Taste.)
Details TBC
12:00 - 13:00, Contributed talks by PDRAs / PhD students
12:00 - 13:00, Contributed talks by PDRAs / PhD students
Title: Sharp asymmetric vertex Ramsey properties of random hypergraphs.
Abstract: In 1992, Luczak, Rucinski and Voigt showed that for any graph H, a parameter m_1(H) - called the 1-density - governs the threshold at which the binomial random graph G(n,p) inherits the vertex Ramsey property for H. In 2000, Freidgut and Krivelevich showed this threshold is sharp. In 1996, Kreuter showed that for any graphs H_1, ..., H_r, a parameter dependent on the two 'densest' of these r graphs governs the threshold at which G(n,p) inherits the 'asymmetric' vertex Ramsey property for H_1, ..., H_r. We prove that this threshold is sharp (as long as the graphs respect some natural balancedness conditions), including in the analogous hypergraph setting.
Joint work with Robert Hancock, Matthew Jenssen and Mael Kupperschmidt.
Details TBC
12:40 - 13:00, Kushankur Dutta, University of Nottingham
12:40 - 13:00, Kushankur Dutta, University of Nottingham
Details TBC
13:00 - 14:30, Lunch (Sandwiches, catered by PJ Taste.)
13:00 - 14:30, Lunch (Sandwiches, catered by PJ Taste.)
Title: Barak-Erdos directed random graphs and related models: limit theorems, perfect simulation and around.
Abstract: We consider directed random graphs, the prototype of which being the Barak-Erdős graph on the integers, and study the way that long (or heavy, if weights are present) paths grow. This is done by relating the graphs to certain particle systems that we call Infinite Bin Models (IBM). We formulate a number of limit theorems. Regenerative techniques are used where possible, exhibiting random sets of vertices over which the graphs regenerate. When edges have random weights we show how the last passage percolation constants behave and when central limit theorems exist. When the underlying vertex set is partially ordered, new phenomena occur, e.g., there are relations with last passage Brownian percolation. We also look at weights that may possibly take negative values and study in detail some special cases that require combinatorial/graph theoretic techniques that exhibit some interesting non-differentiability properties of the last passage percolation constant. We also explain how to approach the problem of estimation of last passage percolation constants by means of perfect simulation.
The talk is based on a series of joint papers with Takis Konstantopoulos, Bastien Mallein, Sanjay Ramassami, James Martin, Denis Denisov, and several other colleagues, and in particular on the survey paper https://arxiv.org/abs/2312.02884
15:30 - 16:00, Refreshments (tea/coffee + biscuits, catered by PJ Taste.)
15:30 - 16:00, Refreshments (tea/coffee + biscuits, catered by PJ Taste.)
Details TBC
Registration
Registration
Registration is free but compulsory for catering purposes. You can register using the link here: https://forms.gle/kmCZpa2V3e6jWGFT8
Location
Location
All talks will take place in Lecture Theatre A of the School of Mathematical and Physical Sciences located in Hicks Building. This room is located at the south entrance to the Hicks Building by the Harley Pub (down the hill from the main entrance.) Helpful images are below.
Address: Hicks Building, Hounsfield Road, Sheffield, S3 7RH
The red box on the right hand side is Sheffield's train station. The red circle on the left is the School of Mathematical and Physical Sciences. Distance between the two is a 15-20 minute walk, or a short trip on the Blue tram line to the "University of Sheffield" stop.
Here you can see the School of Mathematical and Physical Sciences (Hicks Building) and a red arrow indicating the entrance where you will find Lecture Theatre A.
Hotels in the area
Hotels in the area
Below are a few hotels in the area for those of you who intend to stay overnight in Sheffield.
Funding bodies
Funding bodies
This meeting is generously supported by a grant from the Heilbronn Institute for Mathematical Research and the Engineering and Physical Sciences Research Council. The University of Sheffield has supplied physical and online facilities for this workshop. The Applied Probability Trust is providing administrative and organisational support for this meeting.
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