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master's thesis
Prolaznost i povratnost slučajnih šetnji na grafovima
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:305520
Grill, Hrvoje
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Grill, H. (2019). Prolaznost i povratnost slučajnih šetnji na grafovima (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:305520

Grill, Hrvoje. "Prolaznost i povratnost slučajnih šetnji na grafovima." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:305520

Grill, Hrvoje. "Prolaznost i povratnost slučajnih šetnji na grafovima." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:305520

Grill, H. (2019). 'Prolaznost i povratnost slučajnih šetnji na grafovima', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:305520

Grill H. Prolaznost i povratnost slučajnih šetnji na grafovima [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:305520

H. Grill, "Prolaznost i povratnost slučajnih šetnji na grafovima", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:305520

Metadata
TitleProlaznost i povratnost slučajnih šetnji na grafovima
AuthorHrvoje Grill
MentorNikola Sandrić (mentor)
Committee memberNikola Sandrić (predsjednik povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
Committee memberGoran Radunović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-04-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Tema ovog diplomskog rada je prolaznost i povratnost slučajnih šetnji na grafovima. Diplomski rad je podijeljen u tri poglavlja. U prvom poglavlju cilj je upoznati se s Markovljevim lancima i njihovim osnovnim svojstvima. Također, uvodimo pojmove kao što su povratnost, prolaznost i reverzibilnost. U drugom poglavlju uvodimo pojam grafa te se upoznajemo s osnovnim pojmovima vezanim za graf. Uvodimo slučajnu šetnju na grafu i na električnoj mreži. Također, uvodimo pojam energije. U trećem poglavlju dajemo kriterij za prolaznost i povratnost reverzibilnog Markovljevog lanca. Također, dajemo i dovoljan uvjet za povratnost Markovljevog lanca poznat kao Nash-Williamsov kriterij. Zatim, dajemo teorem koji, uz neke dodatne pretpostavke na Markovljev lanac X, daje dovoljne uvjete za prolaznost tog lanca. Za kraj, dajemo nekoliko primjera.
Abstract (english)
The topic of this thesis is transience and recurrence of random walks on graphs. The thesis is divided into three chapters. In the first chapter, the goal is to get acquainted with Markov chains and their basic properties. We also introduce the notions of recurrence, transience and reversibility. In the second chapter, we introduce the concept of a graph and get familiar with the basic concepts related to graphs. We introduce the notion of a random walk on a graph and on the electrical network. In the third chapter, we give a criterion for recurrence and transience of Markov chains. We also provide sufficient conditions for the recurrence of Markov chains known as the Nash-Williams criterion. Then we give a theorem which, with some additional assumptions on the Markov chain X, provides sufficient conditions for transience of that chain. We conclude the thesis with several examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:305520
Study programmeTitle: Mathematical Statistics
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 on2019-07-19 10:02:48