Free probability aspect of irreducible meandric systems, and some related observations about meanders
2016 ◽
Vol 19
(02)
◽
pp. 1650011
Keyword(s):
We consider the concept of irreducible meandric system introduced by Lando and Zvonkin. We place this concept in the lattice framework of [Formula: see text]. As a consequence, we show that the even generating function for irreducible meandric systems is the [Formula: see text]-transform of [Formula: see text], where [Formula: see text] and [Formula: see text] are classically (commuting) independent random variables, and each of [Formula: see text] has centred semicircular distribution of variance [Formula: see text]. Following this point of view, we make some observations about the symmetric linear functional on [Formula: see text] which has [Formula: see text]-transform given by the even generating function for meanders.
1997 ◽
Vol 08
(05)
◽
pp. 645-664
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2014 ◽
Vol 59
(2)
◽
pp. 553-562
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1985 ◽
Vol 29
(4)
◽
pp. 707-718
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Keyword(s):
1965 ◽
Vol 2
(02)
◽
pp. 352-376
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1991 ◽
Vol 14
(2)
◽
pp. 381-384
Keyword(s):
1962 ◽
Vol 57
(297)
◽
pp. 33-45
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