COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

## Phase transition in loop percolationAdd to your list(s) Download to your calendar using vCal - Dr Artem Sapozhnikov, Max-Planck Institut fur Mathematik, Leipzig
- Tuesday 27 May 2014, 16:30-17:30
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact clc32. We study properties of clusters formed by a Poisson ensemble of Markovian loops on $Z^d$ ($d\geq 3$). The intensity measure of the ensemble is proportional to a parameter $\alpha$ which measures the amount of loops entering the picture. First, we observe a non-trivial percolation phase transition with respect to $\alpha$. Then, we focus on the tails of the distributions of the diameter and the size of clusters in the subcritical regime, which decay at most polynomially through the whole domain. We show that for $d\geq 5$, if the cluster of the origin is large, then it will typically contain very close to the origin a loop comparable in diameter and in size with the whole cluster. On the other hand, for the dimensions $3$ and $4$, if the cluster of the origin is large, then typically, there are no large loops near the origin. This phenomenon affects values of various critical exponents: they do not depend on $\alpha$ if the dimension is at least 5, but do depend on $\alpha$ if the dimension is $3$. We conclude with some open questions. Joint work with Yinshan Chang (MPI Leipzig). This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS info aggregator
- DPMMS lists
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB
- Probability
- School of Physical Sciences
- Statistical Laboratory info aggregator
Note that ex-directory lists are not shown. |
## Other listsPeter Whittle Colloquium Invitation George Pitt-Rivers Seminar Series## Other talksParacelsus' Chickens - Strange Tales from the History of Chemistry Transcriptional control of pluripotent stem cell fate by the Nucleosome Remodelling and Deacetylation (NuRD) complex The importance of seed testing Paediatric malignancies: an overview Coordination and inequalities in agglomeration payments: evidence from a laboratory experiment The world is not flat: towards 3D cell biology and 3D devices |