Stationary Eden model on groups
We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and by relying on ergodic theorems, we prove that almost surely all trees are finite. Using the mass tra...
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| creator | Antunović, Tonći Procaccia, Eviatar B |
| description | We consider two stationary versions of the Eden model, on the upper half
planar lattice, resulting in an infinite forest covering the half plane. Under
weak assumptions on the weight distribution and by relying on ergodic theorems,
we prove that almost surely all trees are finite. Using the mass transport
principle, we generalize the result to Eden model in graphs of the form
$G\times\mathbb{Z}_+$, where $G$ is a Cayley graph. This generalizes certain
known results on the two-type Richardson model, in particular of Deijfen and
H\"aggstr\"om in 2007. |
| doi_str_mv | 10.48550/arxiv.1410.4944 |
| format | Article |
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planar lattice, resulting in an infinite forest covering the half plane. Under
weak assumptions on the weight distribution and by relying on ergodic theorems,
we prove that almost surely all trees are finite. Using the mass transport
principle, we generalize the result to Eden model in graphs of the form
$G\times\mathbb{Z}_+$, where $G$ is a Cayley graph. This generalizes certain
known results on the two-type Richardson model, in particular of Deijfen and
H\"aggstr\"om in 2007.</description><identifier>DOI: 10.48550/arxiv.1410.4944</identifier><language>eng</language><subject>Mathematics - Probability</subject><creationdate>2014-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1410.4944$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1410.4944$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Antunović, Tonći</creatorcontrib><creatorcontrib>Procaccia, Eviatar B</creatorcontrib><title>Stationary Eden model on groups</title><description>We consider two stationary versions of the Eden model, on the upper half
planar lattice, resulting in an infinite forest covering the half plane. Under
weak assumptions on the weight distribution and by relying on ergodic theorems,
we prove that almost surely all trees are finite. Using the mass transport
principle, we generalize the result to Eden model in graphs of the form
$G\times\mathbb{Z}_+$, where $G$ is a Cayley graph. This generalizes certain
known results on the two-type Richardson model, in particular of Deijfen and
H\"aggstr\"om in 2007.</description><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzjsPgjAUBeAuDgbdnZQ_AFLaXuhoCD4SEgfZyS0thoRXAI3-e0GdTs4ZTj5CNtRzeSiEt8f-VT5dyudBcr4ku9uIY9k22L_tWJvGrlttKrtt7HvfPrphRRYFVoNZ_9Mi6TFOo7OTXE-X6JA4CII7wMFIGjL0pQhAMulRjVRrlePUKTUQKsM0SqNyKLgoAoCAQSEY94Epyiyy_d1-gVnXl_UkymZoNkPZB8aANnc</recordid><startdate>20141018</startdate><enddate>20141018</enddate><creator>Antunović, Tonći</creator><creator>Procaccia, Eviatar B</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20141018</creationdate><title>Stationary Eden model on groups</title><author>Antunović, Tonći ; Procaccia, Eviatar B</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a654-646e9183a2957693901da1ddbca57611e68be3da9ebc6f45f766736f534263b13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Antunović, Tonći</creatorcontrib><creatorcontrib>Procaccia, Eviatar B</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Antunović, Tonći</au><au>Procaccia, Eviatar B</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stationary Eden model on groups</atitle><date>2014-10-18</date><risdate>2014</risdate><abstract>We consider two stationary versions of the Eden model, on the upper half
planar lattice, resulting in an infinite forest covering the half plane. Under
weak assumptions on the weight distribution and by relying on ergodic theorems,
we prove that almost surely all trees are finite. Using the mass transport
principle, we generalize the result to Eden model in graphs of the form
$G\times\mathbb{Z}_+$, where $G$ is a Cayley graph. This generalizes certain
known results on the two-type Richardson model, in particular of Deijfen and
H\"aggstr\"om in 2007.</abstract><doi>10.48550/arxiv.1410.4944</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Probability |
| title | Stationary Eden model on groups |
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