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DTSTART:20191027T030000
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UID:calendar.22613.field_ns_calendar_date.0@www.lu.se
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DESCRIPTION:A\n \n \n\n \n\nLocation: \n\nthe internet: https://lu-se.
zoom.us/j/397198621\n\nDate: \n\nmåndag\, april 6\, 2020 - 10:15 till 11:3
0\n\n\nViktoria Xing presents her master thesis 'Dynamical Borel–Cantelli
Lemmas and Applications'.\n\n\n\n\nAbstract: The classical Borel–Cantelli
lemma is a beautiful discovery with wide applications in the mathematical
field. The Borel–Cantelli lemmas in dynamical systems are particularly fas
cinating. Here\, D. Kleinbock and G. Margulis have given an important suff
icient condition for the strongly Borel–Cantelli sequence\, which is based
on the work of W. M. Schmidt.\n\nThis Master’s thesis deals with an impr
ovement of Kleinbock’s and Margulis’ theorem and obtains a weaker sufficie
nt condition for the strongly Borel–Cantelli sequences. Several versions o
f the dynamical Borel–Cantelli lemmas will be deduced by extending another
useful theorem by W. M. Schmidt\, W. J. LeVeque\, and W. Philipp.\n\nFurt
hermore\, some applications of our theorems will be discussed. Firstly\, a
characterization of the strongly Borel–Cantelli sequences in one-dimensio
nal Gibbs–Markov systems will be established. This will improve the theore
m of C. Gupta\, M. Nicol\, and W. Ott in. Secondly\, N. Haydn\, M. Nicol\,
T. Persson\, and S. Vaienti proved the strong Borel–Cantelli property in
sequences of balls in terms of a polynomial decay of correlations for Lips
chitz observables. Our theorems will be applied to relax their inequality
assumption. Finally\, as a result of Y. Guivarch’s and A. Raugi’s findings
\, we know that the weakly mixing property could be characterized by Borel
–Cantelli sequences that only contain a finite number of distinct sets wit
h positive measure. This is a Borel–Cantelli result\, although not strong.
So a weakly β-mixing property will be introduced to imply the strong Bore
l–Cantelli property.\n\n \n\nThe presentation will be done with video over
the internet\, using zoom.\n\nLink: https://lu-se.zoom.us/j/397198621\n\n
You may contant Tomas Persson if you want\, tomasp [at] maths [dot] lth [d
ot] se.\n\nCategory: \n\nSeminarium\n\nContact: \n\ntomasp@maths.lth.se
DTSTART;TZID=Europe/Copenhagen:20200406T101500
DTEND;TZID=Europe/Copenhagen:20200406T113000
LAST-MODIFIED:20200331T152845Z
LOCATION:the internet: https://lu-se.zoom.us/j/397198621
SUMMARY:Master thesis presentation\, Viktoria Xing
URL;TYPE=URI:https://www.lu.se/event/master-thesis-presentation-viktoria-xi
ng-0
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