Introduction to Percolation Theory (Part A) Armin Bunde and Jan W ...

RE; S ³EUn»WVm… S U ³ “ »
S ³gi…r^m“ŒfHdQ$e^Q_
S-‰7ˆr†ugko`Qf-dJ^KktfekU = Z ‰ “š…q^Q_o^¨‡ [#" ¸hlk‡gi…q^%$aËiÏHÌQÐ}Ï-ÎP>£¦¡—Ê?¥Jz¢£NÍ>¥Í&$+ЦqÊËiÏ¥eÍ>¡
gib
S ³gibºQ‡@DŒ-¸: ŽH¹ Sgo…r^t_i^xkn†rd„gokbHv–j †rst^Q_ohl`Qf-d
›œ…r^‡vw_afH`Fgaf-dEpuhJst^Qjqkih„bej
bHst~qf-_afVgoh„e^QdJyknhJst~rdJ^H‰-…rbV“Œ^Qe^Q_x‰|hJk#go…r^Cko`QfHd„hJjr€ˆ^K…qf| h„be†r_Eb-vRf˜—³ Un»WVc‰H“š…rhlà…—pu^QjrbHgi^xk#gi…r^
7
$H^K_>kngofH_ngo^Kp”z-¤ hJjq`c^
~r_obHˆqfHˆrhJd„h„gƒyb-vˆ;^QhJjr€‰-fVvµgi^K_¨U”gihJst^œkngi^K~qkK‰-fVg>gi…r^škihŽgo^Œ“š…q^Q_o^7go…r^œ_ofHjqpubHs“œf-d
8 mË¢¡¤£¦¥¨§©¥eÊ Ï¥ Ï¥‡Ï¥qÐ1ÊcÎ rÏVËVÐ
hJjq`c^¤ƒ†rst~qkfVg¦puh„ž;^K_i^Kjgkngi^Q~k :f-jqp ¡ fH_i^ †rjq`QbH_o_i^KdJf-gi^KpX‰q“Œ^ …qf|e^ R © © "!
Vi…£¢
"! ‰”f-jp
¤
hJjqkngi^QhJj+_i^KdJf-gihJbHj
“Œ^beûgofHh„j+go…r^¥
“š…rhlà… hJkš^x½†rh„VfHd„^KjegšgobŸ>hJ`B$¥¤ kŒq_okng¢dlf|“
³Nki^Q^ki^K`cgihJbHjŠrz Ḩ»cz_#¢bHgi^go…qfVg¢^x½z[³ “ »ŒhlkšhJjqpu^K~^Kjqpu^Qjg
b-v>gi…q^puh„st^KjqknhJbHj¨‡—bHv5gi…q^¦dJf-gngihl`c^ez
dJ^Qjr€Hgi…qk‡b-vCgi…r^ kƒgo^Q~qk‡bHv¢gi…r^+_af-jqpubes$“ŒfHdQ$e^Q_‡stf|y¡Vf-_oyH‰
{1jÇgi…q^˜€e^Qjr^K_ofHdŒ`KfHki^H‰>“š…r^Qjgi…r^
^K½;zX³ “ »Œhlkšstb prhŽq^xp+h„jgib
%hJkŒgo…r^pu^Qjknh„gƒyf-jp¦gi…r^à…qfH_i€e^mbHv[go…r^puh„ž;†knhJjr€t~qf-_igihl`cdJ^KkKz
“š…r^K_i^
stbe_i^‡`cbHst~rdJ^cgo^—pu^Kko`c_oh„~rgihJbHjbHv gi…q^tprhŽžS†qkih„bej:~r_obu`c^xkikmhJk~;bekoknhJˆrdJ^ “šh„gi…:gi…q^‡~q_ibeˆqf-ˆrhJdJhŽgƒy
Å
˜—³E; Un»F‰q“š…q^Q_o^I˜—³E; Un»)‡9;—hJkœgo…r^~r_obHˆf-ˆrhJd„h„gƒybHv#qjqpuhJjr€—go…r^“œf-d $H^Q_¢f-vµgi^K_AUŒgihJs‡^ kƒgo^Q~qk
pu^Kjqknh„gƒÿ
;vw_obHs hŽgak‘kngofH_ngoh„jr€ ~;bHhJjgKz[›œ…q^—s‡^xf-j/ko½e†f-_o^tprhJki~rdlfH`c^Kst^Qjg‘`QfHj
fVg‘fkih„gi^“šh„gi…rhJjÇpuhlkƒgaf-jq`Q^
ˆ;^bHˆrgof-hJjr^xp%vw_ibes ˜—³E; Un»¦ hlfDRE;TS³EUn»VN…¤‡ T ;TS1˜—³ŸqbH_ U ¡ ;‰E˜—³E; Un»¦hlk‘pr^Kko`c_oh„ˆ;^Kp¡ˆ y
ff-†qkoknhlf-jv‰E˜—³~r_obHˆqfHˆrh„dJh„gƒy¡pr^QjqkihŽgƒy=à…qf-_afH`cgi^Q_ohQ^Kkgi…r^
puh„ž;†knhJbHj bHj+_o^Q€H†qdJfH_ŒdlfVgigihl`c^xkQz0#C^cŠ g¢“–^`QbHjqkihlpu^Q_špuhlknbe_opr^Q_o^Kpkngi_o†q`cgi†r_o^KkKz
L;M!
+\–Y[¬x\NU;P¤UP«¯7©TVZHU;°N±uRx\NU;P¤ZH°NY>¬KRK©TV¬
“šh„gi…—go…r^¢hJjuqjrh„gi^m~^K_o`QbHdlfVgihJbHj`Qd„†kƒgo^Q_7f-g gi…r^`c_ohŽgohJ`Kf-d;`cbHj`c^Qjgo_of-gihJbHj¿;ÈKze›œ…r^m`cdJ†qkƒgo^Q_
%^mkngof-_ig
bH~qkœf-jpprfHjr€HdJh„jq€‘^QjprkQ‰ufHjqp—ˆ;b-gi… ki†rˆqkngi_o†q`Fgo†r_i^xk–kidJbV“©pubV“šj—gi…q^stbHgihJbHjbHv5f‘_af-jpubHs
…qfek7dJb
$H^Q_xz m†r^˜gib:ki^Qd„vµ‚1knhJsth„dlf-_ohŽgƒye‰5dJb bH~qk‡f-jqpprf-jr€ed„hJjr€•^Kjqprk bu`Q`c†q_ bejf-dJd–dJ^Qjq€-gi…=ki`Kf-dJ^KkK‰[f-jp
“œf-d
“œf-d $H^Q_–hJkœkid„bV“Œ^KppubV“šjbHj¡ÏVεÎd„^Kjr€-go…˜ko`QfHd„^xkQz ›œ…r^mgihJs‡^
gi…q^Q_o^cvwbH_o^¢go…r^s‡bHgihJbHj˜b-vXgo…r^m_af-jpubHs
¦7ÏVÎ ©¡Ž·e‰ƒ¸|¹}z ŸqbH_œgo…r^¦st^Kf-jr‚}ko½†qf-_o^prhJki~rdlfH`c^Kst^Qjgœgi…rhlkšy h„^KdJpqkšh„stst^KprhJf-gi^QdJy
kih„s †rdJf-gihJbHjqkt`Kf-jˆ;^+vwbH†rjphJjgaf-ˆrdJ^¡·HzEŸrbe_—`cbHjgoh„j †r†rs
~^K_o`QbHdlfVgihJbHj3³’¤ “šhlkik—à…q^Q^Kki^+s‡bupu^Kdl»
‡ … ºq‰ ‡)[hJk ^Qjq…qf-jq`Q^Kp‰L‡)[ … Ž ‘ ¸/ ’ ¹}z Ch„žS†qknhJbHj=~r_ob `Q^Kkokn^xk‘pu^xki`Q_ihJˆ;^KpLj y¡^K½;zš³ƒ·|Ḩ»‘f-_o^
hJj
©G©Dz¢£NÍ>¥ ³’`Fvƒzqà…f-~ugo^Q_Še»cz
€H^Kjr^Q_af-dJdJy—_i^Qvw^Q_o_i^xp—gibfekÏ>¥SÍ>¡—ÏV΄ͩDzN>£
›œ…r^¢~r_obHˆqfHˆrhJd„h„gƒy pu^KjqkihŽgƒy Rf˜—³