References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Limit Theorems for Ergodic Group Actions and Random WalksPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2009 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH , 2009. , vii, 18 p.
##### Series

Trita-MAT. MA, ISSN 1401-2278 ; 09:06
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-10451OAI: oai:DiVA.org:kth-10451DiVA: diva2:217655
##### Public defence

2009-05-26, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 13:00 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt455",{id:"formSmash:j_idt455",widgetVar:"widget_formSmash_j_idt455",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt461",{id:"formSmash:j_idt461",widgetVar:"widget_formSmash_j_idt461",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt467",{id:"formSmash:j_idt467",widgetVar:"widget_formSmash_j_idt467",multiple:true});
##### Note

QC 20100705Available from: 2009-05-18 Created: 2009-05-15 Last updated: 2012-03-27Bibliographically approved
##### List of papers

This thesis consists of an introduction, a summary and 7 papers. The papers are devoted to problems in ergodic theory, equidistribution on compact manifolds and random walks on groups.

In Papers A and B, we generalize two classical ergodic theorems for actions of abelian groups. The main result is a generalization of Kingman’s subadditive ergodic theorem to ergodic actions of the group Zd.

In Papers C,D and E, we consider equidistribution problems on nilmanifolds. In Paper C we study the asymptotic behavior of dilations of probability measures on nilmanifolds, supported on singular sets, and prove, under some technical assumptions, effective convergences to Haar measure. In Paper D, we give a new geometric proof of an old result by Koksma on almost sure equidistribution of expansive sequences. In paper E we give necessary and sufficient conditions on a probability measure on a homogeneous Riemannian manifold to be non–atomic.

Papers F and G are concerned with the asymptotic behavior of random walks on groups. In Paper F we consider homogeneous random walks on Gromov hyperbolic groups and establish a central limit theorem for random walks satisfying some technical moment conditions. Paper G is devoted to certain Bernoulli convolutions and the regularity of their value distributions.

1. The asymptotic shape theorem for generalized first passage percolation$(function(){PrimeFaces.cw("OverlayPanel","overlay328522",{id:"formSmash:j_idt503:0:j_idt507",widgetVar:"overlay328522",target:"formSmash:j_idt503:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Ergodic Theorems for Homogeneous Dilations$(function(){PrimeFaces.cw("OverlayPanel","overlay328526",{id:"formSmash:j_idt503:1:j_idt507",widgetVar:"overlay328526",target:"formSmash:j_idt503:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Equidistribution of dilations of polynomial curves in nilmanifolds$(function(){PrimeFaces.cw("OverlayPanel","overlay328532",{id:"formSmash:j_idt503:2:j_idt507",widgetVar:"overlay328532",target:"formSmash:j_idt503:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Almost sure equidistribution in expansive families$(function(){PrimeFaces.cw("OverlayPanel","overlay328533",{id:"formSmash:j_idt503:3:j_idt507",widgetVar:"overlay328533",target:"formSmash:j_idt503:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Continuous Measures on Homogeneous Spaces.$(function(){PrimeFaces.cw("OverlayPanel","overlay328537",{id:"formSmash:j_idt503:4:j_idt507",widgetVar:"overlay328537",target:"formSmash:j_idt503:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

6. Central Limit Theorems for Gromov Hyperbolic Groups$(function(){PrimeFaces.cw("OverlayPanel","overlay328552",{id:"formSmash:j_idt503:5:j_idt507",widgetVar:"overlay328552",target:"formSmash:j_idt503:5:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

7. Almost sure absolute continuity of Bernoulli convolutions$(function(){PrimeFaces.cw("OverlayPanel","overlay278692",{id:"formSmash:j_idt503:6:j_idt507",widgetVar:"overlay278692",target:"formSmash:j_idt503:6:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});