Dear All,

Tomorrow's speakers in the One World Probability Seminar are Peter
Mörters and Markus Heydenreich.
(Note: all times are in UTC. Due to time changes, you should check what
that translates to in your location)
------------------------------------------------

(14:00-15:00 UTC)  Speaker: Peter Mörters

Percolation phase transition in random connection models I: Subcritical
phase in weight-dependent models

We investigate spatial random graphs defined on the points of a Poisson
process in d-dimensional space, which combine scale-free degree
distributions and long-range effects. Every Poisson point is assigned an
independent weight. Given the weight and position of the points, we form
an edge between any pair of points independently with a probability
depending on the two weights of the points and their distance.
Preference is given to short edges and connections to vertices with
large weights. We characterize the parameter regime where there is a
nontrivial percolation phase transition and show that it depends not
only on the power-law exponent of the degree distribution but also on a
geometric model parameter. Based on joint work with Peter Gracar and
Lukas Luechtrath.

(15:00-16:00 UTC) Speaker: Markus Heydenreich

Percolation phase transition in random connection models II: Critical
behaviour for weight-independent models

We study the random connection model (without weights) in a regime where
a percolation phase transition occurs: for low edge density there are
finite connected components only, while for large density there is an
infinite component a.s. Our interest is on the transition between the
low- and high-density regime. We prove an infrared bound for the
critical connection function if the dimension is sufficiently large or
if the pair connectivity has sufficiently slow decay; this allows a
detailed description of this transition. To this end, we devise the lace
expansion for Poisson processes. Based on joint work with Remco van der
Hofstad, Günter Last, and Kilian Matzke.


The zoom link will appear the day before on the OWPS website:
https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.owprobability.org%2Fone-world-probability-seminar&data=04%7C01%7Cowps%40lists.bath.ac.uk%7C51d37e90d03b4b05fa9b08d8ff4a9ac3%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637540043183249689%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=k0reXTQTYMU3hxzzdiPADD4w6hvi7f9gX331wG4PutE%3D&reserved=0

It can also be directly accessed through the link below:

https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Ftum-conf.zoom.us%2Fj%2F65641768006&data=04%7C01%7Cowps%40lists.bath.ac.uk%7C51d37e90d03b4b05fa9b08d8ff4a9ac3%7C377e3d224ea1422db0ad8fcc89406b9e%7C0%7C0%7C637540043183249689%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=%2FTL9zMR1J77RVqtW9FF%2BKCnit%2Fg7K0fnxnp8xEiSvdE%3D&reserved=0

Meeting-ID: 656 4176 8006
Kenncode: 161076

Best wishes,

Julien and Nina