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SUMMARY:Long-range voter model on the real line
DTSTART;VALUE=DATE-TIME:20220805T093000Z
DTEND;VALUE=DATE-TIME:20220805T095000Z
DTSTAMP;VALUE=DATE-TIME:20240625T045529Z
UID:indico-contribution-205-1228@conference2.aau.at
DESCRIPTION:In the voter model on $\\mathbb{Z}$ a countable number of peop
le (called voters) have two opinions\, say $0$ or $1$\, and each voter is
placed at a site of $\\mathbb{Z}$. Each person has an exponential distribu
ted clock. If the clock rings the voter adopts the opinion of a randomly c
hosen neighbour. It is well known that this process satisfies a moment dua
lity with a coalescing random walk. We are interested in a situation where
an uncountable number of voters is placed on the real line and we allow t
hat they adopt their opinion of other voters that are far away. Hence we t
hink of a measure valued process satisfying a moment duality relation with
a coalescing system of symmetric $\\alpha$-stable processes with $\\alpha
\\in (1\,2)$. Such a process has been constructed by Steven N. Evans in 1
997 where he allows more general coalescing mechanisms and infinitely many
opinions. In the talk I will introduce the process and talk about some fr
actional properties. This is joint work in progress with my supervisor Ach
im Klenke and with Leonid Mytnik.\n\nhttps://conference2.aau.at/event/131/
contributions/1228/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1228/
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SUMMARY:Hegelsmann-Krause model with environmental noise
DTSTART;VALUE=DATE-TIME:20220805T090000Z
DTEND;VALUE=DATE-TIME:20220805T092000Z
DTSTAMP;VALUE=DATE-TIME:20240625T045529Z
UID:indico-contribution-205-1231@conference2.aau.at
DESCRIPTION:With the rapid development of the internet and social networks
in the last decades\, more people than ever can express and share their o
pinions. Even though everyone has access to this information\, algorithms
filter the opinions such that viewpoints\, which lie outside your core bel
iefs\, get ignored. The field of opinion dynamics describes such phenomeno
n through bounded confidence models. Based on the Hegelsmann-Krause model
introduced by Rainer Hegelsmann and Ulrich Krause in 2002 we present a tim
e continuous system of interacting particles\, which is driven by idiosync
ratic and environmental noise. In the limit we derive McKean-Vlasov equati
on. By employing a dual argument\, the Ito-Wentzell formula in combination
with reducing the time integrability via stopping time we show the existe
nce and uniqueness of the non-local\, non-linear McKean-Vlasov equation. M
oreover\, we present the propagation of chaos for the particle system by u
tilizing the associated stochastic partial differential equation.\n\nhttps
://conference2.aau.at/event/131/contributions/1231/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1231/
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