Pub Date : 2000-07-01DOI: 10.1002/1098-2418(200007)16:4%3C369::AID-RSA6%3E3.0.CO;2-J
C. Cooper, A. Frieze
{"title":"Hamilton cycles in random graphs and directed graphs","authors":"C. Cooper, A. Frieze","doi":"10.1002/1098-2418(200007)16:4%3C369::AID-RSA6%3E3.0.CO;2-J","DOIUrl":"https://doi.org/10.1002/1098-2418(200007)16:4%3C369::AID-RSA6%3E3.0.CO;2-J","url":null,"abstract":"","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124920401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2000-07-01DOI: 10.1002/1098-2418(200007)16:4%3C333::AID-RSA3%3E3.0.CO;2-C
J. Jonasson, Elchanan Mossel, Y. Peres
Draw planes in R3 that are orthogonal to the x axis, and intersect the x axis at the points of a Poisson process with intensity λ; similarly, draw planes orthogonal to the y and z axes using independent Poisson processes (with the same intensity). Taken together, these planes naturally define a randomly stretched rectangular lattice. Consider bond percolation on this lattice where each edge of length is open with probability e−, and these events are independent given the edge lengths. We show that this model exhibits a phase transition: for large enough λ there is an infinite open cluster a.s., and for small λ all open clusters are finite a.s. We prove this result using the method of paths with exponential intersection tails, which is not applicable in two dimensions. The question whether the analogous process in the plane exhibits a phase transition is open. Disciplines Statistics and Probability This journal article is available at ScholarlyCommons: https://repository.upenn.edu/statistics_papers/434 ! " # $ $ &% '( )* %+ , -/.1032/45-/.1432/676 .14 8 9;:<0=2/432/4?>?.1676 @A9 B,CEDF2/9HG#@AI @A6 J 032/9;KL@MI76ON 4=PQD1@AI 6 PQR ST./U#V#@A:<0=4=.19W.1X/S(2F4=Y5Z*@M[=I7@A]N*4=PWD/@MI76 PWR S^./U -/@AI C=6 2/9;@AK _3@M[=I7C32/I`S(aEbdc/e/e1e f*gEh7i`j
在R3中绘制与x轴正交的平面，并在泊松过程的点处与x轴相交，强度为λ;同样，使用独立的泊松过程(具有相同的强度)绘制与y轴和z轴正交的平面。这些平面合在一起，自然地定义了一个随机拉伸的矩形晶格。考虑这种晶格上的键渗透，其中每条长度的边都以e−的概率打开，并且这些事件在给定的边长度下是独立的。我们证明了该模型表现出一个相变:当λ足够大时，存在一个无限开簇，而当λ足够小时，所有开簇都是有限开簇。我们使用具有指数相交尾的路径方法证明了这一结果，该方法不适用于二维。平面上的类似过程是否表现出相变的问题是开放的。这篇期刊文章可以在ScholarlyCommons上找到:https://repository.upenn.edu/statistics_papers/434 !# $ $ &% '()* %+， -/.1032/45-/。1432/676 .14 8 9;;1676 @A9 B,CEDF2/9HG#@AI @A6 J 032/9;KL@MI76ON 4=PQD1@AI 6 PQR ST./ u# V#@A:=?;A@3ï ÙaEbdcLe f_g(=4Wih·ßDX1äkjl ma&eLnV^]N>^#b3No9 Spb3c =VcIq?9 > WrU cIfs = 4 cin # uþyþ(t # u真空断路)ND9va > wx = y z | {i n eþe} y ~ 6þj8h·ßDX1a(~ 6y{ u Wb cL苏W ^ 9 s9 c O问b3c_b cI_n”(u>= (n ND9c吗?N=# = u(1 yu cm+ @ N > ^ = pn (u W W =/ u c9 > cdq b W 9 dbg4a = VaOuþDyb W =9 c=/ = 4 c= 4 cin;N > ^ = 4 cb);aV;@6N > ^ /大众= == ')9 vavn > acE9 > c wcI9 > N= oU3W&9 = VcIN=(x/ = 4 wrn&uAb3ND9DU3c Ne # N= 4 w¡^9 dn4 ^9 vaxndwrb cLa&9 = VcIN3S4U w + 9 f >= wb c)U¢f + b£;ß1 eoUIoe”÷盟iFU UWU cLf_ = VcINka4b3ND9va > &9 > cN > ^ = 9 c=:/ = Vc= Vc N =N U c9 dnd9 ^ = _N”> ^ = U3W= 4 f@a&eLnV ^ N > ^ # b3N _ yþy S4U W 1 c Yb;!S_X Z [b c#”ßr % h·美元ßDX1a一(4 ~ 6@en > ^ / = Vc % b);aV;N > ^ = = =(大众' 39 a N >] NDWb c / a 9 7 U 8 G ^]美元)_ !D“# a”?> a ' b ' 4$?广州G c_ = /美元Z) DdG YeHgfIh 1美元e UUe中U我o3,U eoU e·æ1 e = UOuUiFU÷AomioU我æ1 = onuUi /æ我÷̧我7 U你÷Aomivuo¥U我÷̧我(< n我æiooU eoU < eæ1 e e o̧÷<æ1 U÷奥米o3 U e UeoU < oe UU oe e非统UeoU紫外线¤o÷̧U UiL你o3,æe eæ我UU eæ我÷÷̧U Aomi6
Pub Date : 2000-01-13DOI: 10.1002/(SICI)1098-2418(199701)10:1/2%3C1::AID-RSA1%3E3.0.CO;2-4
P. Flajolet, W. Szpankowski
3. Binary search has the following algorithm. Look at the middle element in an array. If the element is the one begin looked for (the target), return FOUND. Otherwise, if the element is greater than the target, recursively search the lower half of the array. Otherwise, recursively search the upper half of the array. If the array consists of three or fewer elements, perform a linear search of the array, returning FOUND if found and MISSING otherwise. Which of the following recurrence equations describe binary search?
{"title":"Analysis of algorithms","authors":"P. Flajolet, W. Szpankowski","doi":"10.1002/(SICI)1098-2418(199701)10:1/2%3C1::AID-RSA1%3E3.0.CO;2-4","DOIUrl":"https://doi.org/10.1002/(SICI)1098-2418(199701)10:1/2%3C1::AID-RSA1%3E3.0.CO;2-4","url":null,"abstract":"3. Binary search has the following algorithm. Look at the middle element in an array. If the element is the one begin looked for (the target), return FOUND. Otherwise, if the element is greater than the target, recursively search the lower half of the array. Otherwise, recursively search the upper half of the array. If the array consists of three or fewer elements, perform a linear search of the array, returning FOUND if found and MISSING otherwise. Which of the following recurrence equations describe binary search?","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131201547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-10-09DOI: 10.1002/(SICI)1098-2418(200001)16:1%3C85::AID-RSA6%3E3.0.CO;2-H
D. Wilson
We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related to an idea known as PASTA (Poisson arrivals see time averages) in the operations research literature. Because the new algorithm can be run using a read-once stream of randomness, we call it read-once CFTP. The memory and time requirements of read-once CFTP are on par with the requirements of the usual form of CFTP, and for a variety of applications the requirements may be noticeably less. Some perfect sampling algorithms for point processes are based on an extension of CFTP known as coupling into and from the past; for completeness, we give a read-once version of coupling into and from the past, but it remains unpractical. For these point process applications, we give an alternative coupling method with which read-once CFTP may be efficiently used.
{"title":"How to couple from the past using a read-once source of randomness","authors":"D. Wilson","doi":"10.1002/(SICI)1098-2418(200001)16:1%3C85::AID-RSA6%3E3.0.CO;2-H","DOIUrl":"https://doi.org/10.1002/(SICI)1098-2418(200001)16:1%3C85::AID-RSA6%3E3.0.CO;2-H","url":null,"abstract":"We give a new method for generating perfectly random samples from the stationary distribution of a Markov chain. The method is related to coupling from the past (CFTP), but only runs the Markov chain forwards in time, and never restarts it at previous times in the past. The method is also related to an idea known as PASTA (Poisson arrivals see time averages) in the operations research literature. Because the new algorithm can be run using a read-once stream of randomness, we call it read-once CFTP. The memory and time requirements of read-once CFTP are on par with the requirements of the usual form of CFTP, and for a variety of applications the requirements may be noticeably less. Some perfect sampling algorithms for point processes are based on an extension of CFTP known as coupling into and from the past; for completeness, we give a read-once version of coupling into and from the past, but it remains unpractical. For these point process applications, we give an alternative coupling method with which read-once CFTP may be efficiently used.","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"218 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115525582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：