Journal article 1378 views
Equilibrium Kawasaki dynamics and determinantal point process
Journal of Mathematical Sciences, Volume: 190, Issue: 3, Pages: 451 - 458
Swansea University Author:
Eugene Lytvynov
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DOI (Published version): 10.1007/s10958-013-1260-6
Abstract
Let $\mu$ be a point process on a countable discrete space$\mathfrak X$. Under assumption that $\mu$ is quasi-invariant with respect toany finitary permutation of $\mathfrak X$, we describe a general scheme forconstructing an equilibrium Kawasaki dynamics for which $\mu$ is asymmetrizing (and hence...
| Published in: | Journal of Mathematical Sciences |
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| Published: |
2013
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| Online Access: |
http://link.springer.com/article/10.1007/s10958-013-1260-6 |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa19098 |
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| Abstract: |
Let $\mu$ be a point process on a countable discrete space$\mathfrak X$. Under assumption that $\mu$ is quasi-invariant with respect toany finitary permutation of $\mathfrak X$, we describe a general scheme forconstructing an equilibrium Kawasaki dynamics for which $\mu$ is asymmetrizing (and hence invariant) measure. We also exhibit a two-parameterfamily of point processes $\mu$ possessing the needed quasi-invarianceproperty. Each process of this family is determinantal, and its correlationkernel is the kernel of a projection operator in $\ell^2(\mathfrak X)$. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
3 |
| Start Page: |
451 |
| End Page: |
458 |