Bootstrap percolation - 편집 역사

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articles

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찾아 바꾸기 – “4909919” 문자열을 “” 문자열로

@@ 96번째 줄: / 96번째 줄: @@
 [[분류:migrate]]
-== 메타데이터 ==
+==메타데이터==
 ===위키데이터===
 * ID :  [https://www.wikidata.org/wiki/Q25305507 Q25305507]

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-*  one of important question in 2d percolation is the calculation of power-law exponent for boostrap percolation
+*  one of important question in 2d percolation is the calculation of power-law exponent for boostrap percolation
 *  this is related to the theory of partitions without k-gaps
-−
 ==bootstrap percolation==
@@ 13번째 줄: / 13번째 줄: @@
 * http://mathworld.wolfram.com/BootstrapPercolation.html
-−
-−
 ==partitions without k-gaps==
@@ 21번째 줄: / 21번째 줄: @@
 *  partitions without k-gaps (or k-sequences)
 *  p_k(n) is the number of partitions of n that do not contain any sequence of consecutive integers of length k. p_2 (7) = 8.
-*  examples: partition of 7 {{7},{6,1},{5,2},{5,1,1},{4,3},{4,2,1},{4,1,1,1},{3,3,1},{3,2,2},{3,2,1,1},{3,1,1,1,1},{2,2,2,1},{2,2,1,1,1},{2,1,1,1,1,1},{1,1,1,1,1,1,1}} 7, 6 + 1, 5 + 2, 5 + 1 + 1, 4 + 1 + 1 + 1, 3 + 3 + 1, 3 + 1 + 1 + 1 + 1, and 1 + 1 + 1 + 1 + 1 + 1 + 1. so there are 8 partitions without 2-gaps
+*  examples: partition of 7 {{7},{6,1},{5,2},{5,1,1},{4,3},{4,2,1},{4,1,1,1},{3,3,1},{3,2,2},{3,2,1,1},{3,1,1,1,1},{2,2,2,1},{2,2,1,1,1},{2,1,1,1,1,1},{1,1,1,1,1,1,1}} 7, 6 + 1, 5 + 2, 5 + 1 + 1, 4 + 1 + 1 + 1, 3 + 3 + 1, 3 + 1 + 1 + 1 + 1, and 1 + 1 + 1 + 1 + 1 + 1 + 1. so there are 8 partitions without 2-gaps
 *  Anderew's result
 **  generating function for partitions without k-gaps<math>G_2(q)=1+\sum_{n=1}^{\infty}\frac{q^n\prod_{j=1}^{n-1}(1-q^j+q^{2j})}{(q;q)_n}</math>[http://www.research.att.com/%7Enjas/sequences/A116931 A116931]
-#  (*define a gap as 'b' *) b := 2 G[b_, x_] :=  Sum[x^k*Product[1 + x^(b*j)/(1 - x^j), {j, 1, k - 1}]/(1 - x^k), {k,    1, 30}] Series[G[b, x], {x, 0, 20}] Table[SeriesCoefficient[%, n], {n, 0, 20}]
+#  (*define a gap as 'b' *) b := 2 G[b_, x_] :=  Sum[x^k*Product[1 + x^(b*j)/(1 - x^j), {j, 1, k - 1}]/(1 - x^k), {k,    1, 30}] Series[G[b, x], {x, 0, 20}] Table[SeriesCoefficient[%, n], {n, 0, 20}]
 * [[3 q-series|q-series]]
-−
-−
 ==q-series from percolation==
 *  definition<math>P_k(q)=(q;q)_{\infty}G_k(q)</math>
-*  Andrews and Zagier expression of <math>P_k(q)</math>
+*  Andrews and Zagier expression of <math>P_k(q)</math>
-*  result of '''[HLR04]''' if <math>q=e^{-t}</math> and  <math>t\sim 0</math><math>P_k(q) \sim \frac{-\lambda_k}{1-q}</math> as <math>q \to 1</math>
+*  result of '''[HLR04]''' if <math>q=e^{-t}</math> and  <math>t\sim 0</math><math>P_k(q) \sim \frac{-\lambda_k}{1-q}</math> as <math>q \to 1</math>
-−
-−
 ==Andrews' conjecture on asymptotics==
-*  asymptotics of P_2(q) is known <math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<math>P_2(q) \sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{18t})</math>
+*  asymptotics of P_2(q) is known <math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<math>P_2(q) \sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{18t})</math>
-*  conjecture<math>P_k(q) \sim \sqrt\frac{2\pi}{t}\exp(-\frac{\lambda_k}{t})</math> where <math>\lambda_k=\frac{\pi^2}{3k(k+1)}</math>
+*  conjecture<math>P_k(q) \sim \sqrt\frac{2\pi}{t}\exp(-\frac{\lambda_k}{t})</math> where <math>\lambda_k=\frac{\pi^2}{3k(k+1)}</math>
-−
-−
-==tricky integrals==
+==tricky integrals==
-*  Henrik Eriksson: [http://www.math.ubc.ca/~holroyd/integral.pdf A Tricky Integral]<math>f_1(x)=1-x</math><math>f_2(x)=\frac{1-x+\sqrt{(1-x)(1+3x)}}{2}</math>
+*  Henrik Eriksson: [http://www.math.ubc.ca/~holroyd/integral.pdf A Tricky Integral]<math>f_1(x)=1-x</math><math>f_2(x)=\frac{1-x+\sqrt{(1-x)(1+3x)}}{2}</math>
 * <math>\lambda_k=\frac{\pi^2}{3k(k+1)}</math>
 * <math>\lambda_2=\frac{\pi^2}{18}</math>
-−
-−
 ==relevance to dedekind eta function==
-*  Dedekind eta function ([http://pythagoras0.springnote.com/pages/3325777 데데킨트 에타함수])<math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<math>\prod_{n=1}^{\infty}(1-q^n)=1+\sum_{n\geq 1}^{\infty}\frac{(-1)^nq^{n(n+1)/2}}{(q)_n}\sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{6t})</math> more generally, <math>q=\exp(\frac{2\pi ih}{k})e^{-t}</math>  and  <math>t\to 0</math> implies<math>\sqrt{\frac{t}{2\pi}}\exp({\frac{\pi^2}{6k^2t}})\eta(\frac{h}{k}+i\frac{t}{2\pi})\sim  \frac{\exp\left(\pi i (\frac{h}{12k}-s(h,k)\right)}{\sqrt{k}}</math>
+*  Dedekind eta function ([http://pythagoras0.springnote.com/pages/3325777 데데킨트 에타함수])<math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<math>\prod_{n=1}^{\infty}(1-q^n)=1+\sum_{n\geq 1}^{\infty}\frac{(-1)^nq^{n(n+1)/2}}{(q)_n}\sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{6t})</math> more generally, <math>q=\exp(\frac{2\pi ih}{k})e^{-t}</math>  and  <math>t\to 0</math> implies<math>\sqrt{\frac{t}{2\pi}}\exp({\frac{\pi^2}{6k^2t}})\eta(\frac{h}{k}+i\frac{t}{2\pi})\sim  \frac{\exp\left(\pi i (\frac{h}{12k}-s(h,k)\right)}{\sqrt{k}}</math>
-−
-−
 ==related items==
@@ 81번째 줄: / 81번째 줄: @@
 ** [http://arxiv.org/abs/1002.3881 ]Janko Gravner, Alexander E. Holroyd, Robert Morris, 2010
 * [http://arxiv.org/abs/1001.1977 Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolation]
-** [http://arxiv.org/find/math/1/au:+Bringmann_K/0/1/0/all/0/1 Kathrin Bringmann], [http://arxiv.org/find/math/1/au:+Mahlburg_K/0/1/0/all/0/1 Karl Mahlburg], 2010
+** [http://arxiv.org/find/math/1/au:+Bringmann_K/0/1/0/all/0/1 Kathrin Bringmann], [http://arxiv.org/find/math/1/au:+Mahlburg_K/0/1/0/all/0/1 Karl Mahlburg], 2010
 * [http://dx.doi.org/10.1016/j.jcta.2006.06.010 Integrals, partitions and MacMahon's Theorem]
-**  George Andrewsa,  Dan Romik, 2007
+**  George Andrewsa,  Dan Romik, 2007
 *  Slow convergence
 * [http://www.pnas.org/content/102/13/4666.full Partitions with short sequences and mock theta functions]
 **  George E. Andrews, 2005
 * '''[HLR04]'''[http://research.microsoft.com/en-us/um/people/holroyd/papers/int.pdf Integrals, Partitions, and Cellular Automata]
-**  A. E. Holroyd, T. M. Liggett & D. Romik, Transactions of the American Mathematical Society, 2004, Vol 356, 3349-3368
+**  A. E. Holroyd, T. M. Liggett & D. Romik, Transactions of the American Mathematical Society, 2004, Vol 356, 3349-3368
 * [http://www.springerlink.com/content/g420hc5h6qu6e65x/ sharp metastability threshold for two-dimensional bootstrap percolation]
 **  Alexander E. Holroyd, 2003
-−
 [[분류:integrable systems]]
 [[분류:math and physics]]

← 이전 판		2020년 12월 28일 (월) 08:03 판
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	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:migrate]]		[[분류:migrate]]
		+
		+	== 메타데이터 ==
		+
		+	===위키데이터===
		+	* ID : [https://www.wikidata.org/wiki/Q25305507 Q25305507]

@@ 93번째 줄: / 93번째 줄: @@
 [[분류:integrable systems]]
 [[분류:math and physics]]
 [[분류:migrate]]

@@ 65번째 줄: / 65번째 줄: @@
 *  Dedekind eta function ([http://pythagoras0.springnote.com/pages/3325777 데데킨트 에타함수])<math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<math>\prod_{n=1}^{\infty}(1-q^n)=1+\sum_{n\geq 1}^{\infty}\frac{(-1)^nq^{n(n+1)/2}}{(q)_n}\sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{6t})</math> more generally, <math>q=\exp(\frac{2\pi ih}{k})e^{-t}</math>  and  <math>t\to 0</math> implies<math>\sqrt{\frac{t}{2\pi}}\exp({\frac{\pi^2}{6k^2t}})\eta(\frac{h}{k}+i\frac{t}{2\pi})\sim  \frac{\exp\left(\pi i (\frac{h}{12k}-s(h,k)\right)}{\sqrt{k}}</math>
@@ 83번째 줄: / 75번째 줄: @@
 * [[examples of mock theta functions|Ramanujan's mock theta functions]]
 ==articles==
@@ 128번째 줄: / 92번째 줄: @@
 **  Alexander E. Holroyd, 2003
 [[분류:integrable systems]]
 [[분류:math and physics]]
 [[분류:math and physics]]
 [[분류:migrate]]

← 이전 판		2020년 11월 14일 (토) 01:26 판
127번째 줄:		127번째 줄:
	* [http://www.springerlink.com/content/g420hc5h6qu6e65x/ sharp metastability threshold for two-dimensional bootstrap percolation]		* [http://www.springerlink.com/content/g420hc5h6qu6e65x/ sharp metastability threshold for two-dimensional bootstrap percolation]
	** Alexander E. Holroyd, 2003		** Alexander E. Holroyd, 2003
−
−	* [[2010년 books and articles\|논문정리]]
−	* http://www.ams.org/mathscinet
−	* http://www.zentralblatt-math.org/zmath/en/
−	* http://pythagoras0.springnote.com/
−	* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html][http://www.ams.org/mathscinet ]
−	* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
−	* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
−	* http://dx.doi.org/
−

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-*  one of important question in 2d percolation is the calculation of power-law exponent for boostrap percolation<br>
+*  one of important question in 2d percolation is the calculation of power-law exponent for boostrap percolation
-*  this is related to the theory of partitions without k-gaps<br>  <br>
+*  this is related to the theory of partitions without k-gaps
@@ 8번째 줄: / 8번째 줄: @@
 ==bootstrap percolation==
-*  growth rule<br>
+*  growth rule
-* http://www.math.ubc.ca/~holroyd/boot/<br>
+* http://www.math.ubc.ca/~holroyd/boot/
-* http://mathworld.wolfram.com/BootstrapPercolation.html<br>
+* http://mathworld.wolfram.com/BootstrapPercolation.html
@@ 19번째 줄: / 19번째 줄: @@
 ==partitions without k-gaps==
-*  partitions without k-gaps (or k-sequences)<br>
+*  partitions without k-gaps (or k-sequences)
-*  p_k(n) is the number of partitions of n that do not contain any sequence of consecutive integers of length k. p_2 (7) = 8.<br>
+*  p_k(n) is the number of partitions of n that do not contain any sequence of consecutive integers of length k. p_2 (7) = 8.
-*  examples: partition of 7<br> {{7},{6,1},{5,2},{5,1,1},{4,3},{4,2,1},{4,1,1,1},{3,3,1},{3,2,2},{3,2,1,1},{3,1,1,1,1},{2,2,2,1},{2,2,1,1,1},{2,1,1,1,1,1},{1,1,1,1,1,1,1}}<br> 7, 6 + 1, 5 + 2, 5 + 1 + 1, 4 + 1 + 1 + 1, 3 + 3 + 1, 3 + 1 + 1 + 1 + 1, and 1 + 1 + 1 + 1 + 1 + 1 + 1.<br> so there are 8 partitions without 2-gaps<br>
+*  examples: partition of 7 {{7},{6,1},{5,2},{5,1,1},{4,3},{4,2,1},{4,1,1,1},{3,3,1},{3,2,2},{3,2,1,1},{3,1,1,1,1},{2,2,2,1},{2,2,1,1,1},{2,1,1,1,1,1},{1,1,1,1,1,1,1}} 7, 6 + 1, 5 + 2, 5 + 1 + 1, 4 + 1 + 1 + 1, 3 + 3 + 1, 3 + 1 + 1 + 1 + 1, and 1 + 1 + 1 + 1 + 1 + 1 + 1. so there are 8 partitions without 2-gaps
-*  Anderew's result<br>
+*  Anderew's result
-**  generating function for partitions without k-gaps<br><math>G_2(q)=1+\sum_{n=1}^{\infty}\frac{q^n\prod_{j=1}^{n-1}(1-q^j+q^{2j})}{(q;q)_n}</math>[http://www.research.att.com/%7Enjas/sequences/A116931 A116931]<br>
+**  generating function for partitions without k-gaps<math>G_2(q)=1+\sum_{n=1}^{\infty}\frac{q^n\prod_{j=1}^{n-1}(1-q^j+q^{2j})}{(q;q)_n}</math>[http://www.research.att.com/%7Enjas/sequences/A116931 A116931]
-#  (*define a gap as 'b' *)<br> b := 2<br> G[b_, x_] :=<br>  Sum[x^k*Product[1 + x^(b*j)/(1 - x^j), {j, 1, k - 1}]/(1 - x^k), {k,<br>    1, 30}]<br> Series[G[b, x], {x, 0, 20}]<br> Table[SeriesCoefficient[%, n], {n, 0, 20}]<br>
+#  (*define a gap as 'b' *) b := 2 G[b_, x_] :=  Sum[x^k*Product[1 + x^(b*j)/(1 - x^j), {j, 1, k - 1}]/(1 - x^k), {k,    1, 30}] Series[G[b, x], {x, 0, 20}] Table[SeriesCoefficient[%, n], {n, 0, 20}]
-* [[3 q-series|q-series]]<br>
+* [[3 q-series|q-series]]
@@ 35번째 줄: / 35번째 줄: @@
 ==q-series from percolation==
-*  definition<br><math>P_k(q)=(q;q)_{\infty}G_k(q)</math><br>
+*  definition<math>P_k(q)=(q;q)_{\infty}G_k(q)</math>
-*  Andrews and Zagier expression of <math>P_k(q)</math><br>
+*  Andrews and Zagier expression of <math>P_k(q)</math>
-*  result of '''[HLR04]'''<br> if <math>q=e^{-t}</math> and  <math>t\sim 0</math><br><math>P_k(q) \sim \frac{-\lambda_k}{1-q}</math> as <math>q \to 1</math><br>
+*  result of '''[HLR04]''' if <math>q=e^{-t}</math> and  <math>t\sim 0</math><math>P_k(q) \sim \frac{-\lambda_k}{1-q}</math> as <math>q \to 1</math>
@@ 45번째 줄: / 45번째 줄: @@
 ==Andrews' conjecture on asymptotics==
-*  asymptotics of P_2(q) is known <br><math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<br><math>P_2(q) \sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{18t})</math><br>
+*  asymptotics of P_2(q) is known <math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<math>P_2(q) \sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{18t})</math>
-*  conjecture<br><math>P_k(q) \sim \sqrt\frac{2\pi}{t}\exp(-\frac{\lambda_k}{t})</math><br> where <math>\lambda_k=\frac{\pi^2}{3k(k+1)}</math><br>
+*  conjecture<math>P_k(q) \sim \sqrt\frac{2\pi}{t}\exp(-\frac{\lambda_k}{t})</math> where <math>\lambda_k=\frac{\pi^2}{3k(k+1)}</math>
@@ 54번째 줄: / 54번째 줄: @@
 ==tricky integrals==
-*  Henrik Eriksson: [http://www.math.ubc.ca/~holroyd/integral.pdf A Tricky Integral]<br><math>f_1(x)=1-x</math><br><math>f_2(x)=\frac{1-x+\sqrt{(1-x)(1+3x)}}{2}</math><br>
+*  Henrik Eriksson: [http://www.math.ubc.ca/~holroyd/integral.pdf A Tricky Integral]<math>f_1(x)=1-x</math><math>f_2(x)=\frac{1-x+\sqrt{(1-x)(1+3x)}}{2}</math>
-* <math>\lambda_k=\frac{\pi^2}{3k(k+1)}</math><br>
+* <math>\lambda_k=\frac{\pi^2}{3k(k+1)}</math>
 * <math>\lambda_2=\frac{\pi^2}{18}</math>
@@ 64번째 줄: / 64번째 줄: @@
 ==relevance to dedekind eta function==
-*  Dedekind eta function ([http://pythagoras0.springnote.com/pages/3325777 데데킨트 에타함수])<br><math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<br><math>\prod_{n=1}^{\infty}(1-q^n)=1+\sum_{n\geq 1}^{\infty}\frac{(-1)^nq^{n(n+1)/2}}{(q)_n}\sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{6t})</math><br> more generally, <math>q=\exp(\frac{2\pi ih}{k})e^{-t}</math>  and  <math>t\to 0</math> implies<br><math>\sqrt{\frac{t}{2\pi}}\exp({\frac{\pi^2}{6k^2t}})\eta(\frac{h}{k}+i\frac{t}{2\pi})\sim  \frac{\exp\left(\pi i (\frac{h}{12k}-s(h,k)\right)}{\sqrt{k}}</math><br>
+*  Dedekind eta function ([http://pythagoras0.springnote.com/pages/3325777 데데킨트 에타함수])<math>q=e^{-t}</math> 으로 두면 <math>t\sim 0</math> 일 때,<math>\prod_{n=1}^{\infty}(1-q^n)=1+\sum_{n\geq 1}^{\infty}\frac{(-1)^nq^{n(n+1)/2}}{(q)_n}\sim \sqrt\frac{2\pi}{t}\exp(-\frac{\pi^2}{6t})</math> more generally, <math>q=\exp(\frac{2\pi ih}{k})e^{-t}</math>  and  <math>t\to 0</math> implies<math>\sqrt{\frac{t}{2\pi}}\exp({\frac{\pi^2}{6k^2t}})\eta(\frac{h}{k}+i\frac{t}{2\pi})\sim  \frac{\exp\left(\pi i (\frac{h}{12k}-s(h,k)\right)}{\sqrt{k}}</math>
@@ 80번째 줄: / 80번째 줄: @@
 ==related items==
-* [[asymptotic analysis of basic hypergeometric series]]<br>
+* [[asymptotic analysis of basic hypergeometric series]]
-* [[examples of mock theta functions|Ramanujan's mock theta functions]]<br>
+* [[examples of mock theta functions|Ramanujan's mock theta functions]]
@@ 101번째 줄: / 101번째 줄: @@
-* [[2010년 books and articles]]<br>
+* [[2010년 books and articles]]
 * http://gigapedia.info/1/
 * http://gigapedia.info/1/
@@ 114번째 줄: / 114번째 줄: @@
 ==articles==
-* [http://arxiv.org/abs/1002.3881 A sharper threshold for bootstrap percolation in two dimensions]<br>
+* [http://arxiv.org/abs/1002.3881 A sharper threshold for bootstrap percolation in two dimensions]
 ** [http://arxiv.org/abs/1002.3881 ]Janko Gravner, Alexander E. Holroyd, Robert Morris, 2010
-* [http://arxiv.org/abs/1001.1977 Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolation]<br>
+* [http://arxiv.org/abs/1001.1977 Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolation]
-** [http://arxiv.org/find/math/1/au:+Bringmann_K/0/1/0/all/0/1 Kathrin Bringmann], [http://arxiv.org/find/math/1/au:+Mahlburg_K/0/1/0/all/0/1 Karl Mahlburg], 2010<br>
+** [http://arxiv.org/find/math/1/au:+Bringmann_K/0/1/0/all/0/1 Kathrin Bringmann], [http://arxiv.org/find/math/1/au:+Mahlburg_K/0/1/0/all/0/1 Karl Mahlburg], 2010
-* [http://dx.doi.org/10.1016/j.jcta.2006.06.010 Integrals, partitions and MacMahon's Theorem]<br>
+* [http://dx.doi.org/10.1016/j.jcta.2006.06.010 Integrals, partitions and MacMahon's Theorem]
-**  George Andrewsa,  Dan Romik, 2007<br>
+**  George Andrewsa,  Dan Romik, 2007
-*  Slow convergence<br>
+*  Slow convergence
-* [http://www.pnas.org/content/102/13/4666.full Partitions with short sequences and mock theta functions]<br>
+* [http://www.pnas.org/content/102/13/4666.full Partitions with short sequences and mock theta functions]
-**  George E. Andrews, 2005<br>
+**  George E. Andrews, 2005
-* '''[HLR04]'''[http://research.microsoft.com/en-us/um/people/holroyd/papers/int.pdf Integrals, Partitions, and Cellular Automata]<br>
+* '''[HLR04]'''[http://research.microsoft.com/en-us/um/people/holroyd/papers/int.pdf Integrals, Partitions, and Cellular Automata]
-**  A. E. Holroyd, T. M. Liggett & D. Romik, Transactions of the American Mathematical Society, 2004, Vol 356, 3349-3368<br>
+**  A. E. Holroyd, T. M. Liggett & D. Romik, Transactions of the American Mathematical Society, 2004, Vol 356, 3349-3368
-* [http://www.springerlink.com/content/g420hc5h6qu6e65x/ sharp metastability threshold for two-dimensional bootstrap percolation]<br>
+* [http://www.springerlink.com/content/g420hc5h6qu6e65x/ sharp metastability threshold for two-dimensional bootstrap percolation]
-**  Alexander E. Holroyd, 2003<br>
+**  Alexander E. Holroyd, 2003
 * [[2010년 books and articles|논문정리]]
@@ 152번째 줄: / 152번째 줄: @@
 ==blogs==
-*  구글 블로그 검색<br>
+*  구글 블로그 검색
 ** http://blogsearch.google.com/blogsearch?q=
 ** http://blogsearch.google.com/blogsearch?q=

← 이전 판		2012년 11월 2일 (금) 02:51 판
106번째 줄:		106번째 줄:
	* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=		* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

−	~~[[4909919\|4909919]]~~	+