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master's thesis
Razdioba dugih ciklusa i velikih djelitelja
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:297514
Antoliš, Ivana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Antoliš, I. (2015). Razdioba dugih ciklusa i velikih djelitelja (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:297514

Antoliš, Ivana. "Razdioba dugih ciklusa i velikih djelitelja." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:297514

Antoliš, Ivana. "Razdioba dugih ciklusa i velikih djelitelja." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:297514

Antoliš, I. (2015). 'Razdioba dugih ciklusa i velikih djelitelja', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:297514

Antoliš I. Razdioba dugih ciklusa i velikih djelitelja [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:297514

I. Antoliš, "Razdioba dugih ciklusa i velikih djelitelja", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:297514

Metadata
TitleRazdioba dugih ciklusa i velikih djelitelja
AuthorIvana Antoliš
MentorBojan Basrak (mentor)
Committee memberBojan Basrak (predsjednik povjerenstva)
Committee memberNikola Sarapa (član povjerenstva)
Committee memberMiljenko Huzak (član povjerenstva)
Committee memberNela Bosner (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Jedan on ciljeva ovog diplomskog rada bio je definirati Poisson-Dirichletovu razdiobu i proučiti njezina glavna svojstva. Uvedeni su pojmovi iz područja matematičke analize, teorije vjerojatnosti i teorije brojeva nužni za razumijevanje kasnijih rezultata, a neka njihova svojstva su i dokazana. Motivacija i opravdanost definicije Poisson-Dirichletove razdiobe ilustrirani su kroz dva primjera u drugom poglavlju. Detaljno su obrazložena i formalno pokazana asimptotska svojstva slučajnih vektora koji odgovaraju relativnim duljinama ciklusa slučajnih permutacija, odnosno logaritamskih vrijednosti prostih djelitelja slučajnog prirodnog broja manjeg od n. U trećem poglavlju izrečeni su i dokazani glavni rezultati razmatrani u ovom radu. Povezana je funkcija gustoće Poisson-Dirichletove razdiobe, njezine marginalne gustoće i momenti s asimptotskim svojstvima dugih ciklusa i velikih djelitelja. U zadnjem poglavlju su ti rezultati primijenjeni na konkretnim podacima te je ilustrirana brzina konvergencije distribucija dugih ciklusa i velikih djelitelja za velik, ali konačan n.
Abstract (english)
One of the aims of this thesis was to define Poisson-Dirichlet distribution and study its main properties. Concepts from the fields of Analysis, Probability theory and Number theory are introduced and some of their properties proven in order to fully understand later results. The motivation and justification for the definition of Poisson-Dirichlet distribution are illustrated by two examples in Chapter 2. Asymptotic properties of random vectors corresponding to relative lengths of cycles in random permutations and logarithmic values of prime divisors of random natural numbers smaller than n are formally proven and explained in detail. The main results discussed in this thesis are stated and proven in Chapter 3. The relation between probability density function of Poisson-Dirichlet distribution, its marginal densities and moments and asymptotic properties of long cycles and great divisors is proven. In concluding chapter these results are applied to specific data, we also illustrate the speed of convergence of distributions of long cycles and great divisors for large, but finite n.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:297514
Study programmeTitle: Pure Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-05-05 11:21:53