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The Strange Logic of Galton-Watson Trees.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	The Strange Logic of Galton-Watson Trees./
Author:	Podder, Moumanti.
Description:	1 online resource (148 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Contained By:	Dissertation Abstracts International78-12B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355128468

The Strange Logic of Galton-Watson Trees.
Podder, Moumanti.

The Strange Logic of Galton-Watson Trees. - 1 online resource (148 pages)

Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

My dissertation is on the analysis of the probabilities of different classes of properties, parametrized by mathematical logic, on the well-known Galton-Watson (GW) branching porcess with Poisson(lambda) offspring distribution. The first part of my dissertation focuses on probabilities of first order (FO) sentences which capture local structures inside the tree. I give a complete description of the probabilities Plambda[ A] of all possible FO sentences A conditioned on the survival of the GW tree. There are, up to tautology, only a finite number of FO sentences of given quantifier depth k. For an arbitrary k, I introduce a natural distributional recursion Psi k, such that the probabilities of these sentences form a fixed point of Psik. I further show that Psi k is a contraction, and that its fixed point is unique and analytic in lambda.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355128468Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

The Strange Logic of Galton-Watson Trees.
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100 1 $a Podder, Moumanti. $3 1180637
245 1 4 $a The Strange Logic of Galton-Watson Trees.
264 0 $c 2017
300 $a 1 online resource (148 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
500 $a Adviser: Joel Spencer.
502 $a Thesis (Ph.D.) $c New York University $d 2017.
504 $a Includes bibliographical references
520 $a My dissertation is on the analysis of the probabilities of different classes of properties, parametrized by mathematical logic, on the well-known Galton-Watson (GW) branching porcess with Poisson(lambda) offspring distribution. The first part of my dissertation focuses on probabilities of first order (FO) sentences which capture local structures inside the tree. I give a complete description of the probabilities Plambda[ A] of all possible FO sentences A conditioned on the survival of the GW tree. There are, up to tautology, only a finite number of FO sentences of given quantifier depth k. For an arbitrary k, I introduce a natural distributional recursion Psi k, such that the probabilities of these sentences form a fixed point of Psik. I further show that Psi k is a contraction, and that its fixed point is unique and analytic in lambda.
520 $a The second part of my dissertation focuses on existential monadic second order (EMSO) properties of the GW tree. I show that finiteness of the tree is not an EMSO; furthermore, there is no EMSO which can express the finiteness property on all but a measure 0 subset of trees.
520 $a The final part of my dissertation considers the alternating quantifier depths (a.q.d) of Fo sentences. I give a specific sequence {KEIN s} of sentences and show that the a.q.d of KEIN s is precisely s. In particular this implies that the a.q.d hierarchy for this sequence does not collapse.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a New York University. $b Mathematics. $3 1180487
773 0 $t Dissertation Abstracts International $g 78-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10261483 $z click for full text (PQDT)