GENERATING "DEPENDENT" QUASI-RANDOM NUMBERS Shane G ...



 






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 *( ),+.-0/21'3045/-,60/798;:?+.7A@ABC/-D@E:.FHGI-,6*J,8;@A7!KL+.M+.-?6 N>?/O7!+.@AKP:-,8RQS-0TKP-0//O7AKP-0T U -,KWV
½x/{@2œ ËAœ +.-,6{œ ˜Z_`/ñJ0-,KF:07!:m]/O6*J,7A/,7A:07!:_,MW/OB´8A//1)0:D8;)²+-,6 4z/-?6*/798;:07!/VmKP:J,88;/b] @AKP:-`„ 3’/C6*:8A: _mX/{ƒm@!/-,6*KP-0T @A),/2yNrHw ^ BC/{@A),:m6a`+-,6@A/O7AB¨@A)0/}B'/@A)0:*6• U ^ rHw ^ a ‹E)0KL]9)™KL82KP-D@A/O-,6*/O6Œ@A:’_?/BC-0/BC:-,KP] F:7‘A€DJ,+`:?/O-,6*/O-`:-0/O-D@!8u‚…7A/b]+.MPMRF7!:Bû@!)0/ >07!/VmKP:J,8z8A/O]{@AKP:-@!),+l@5@A)0/O7A/}KP8+.-+>0>07!:>07!KP+.@A/-0:@AKP:-u:F ‘;KP-,6*/O>?/O-,6*/O-,]{/b“sKW-²@A)0KL88A/{@A@AKP-0TŒ‹E)0/O7A/u@A)0/’V/O]{@A:0MP/ Vl+.7!KWi +.-,]/34z:l‹d/V/O7Oa~K@}KP82B':0J0@;i KP-0T+.-/b8Y@!KWBZ+l@!/:.F†š›‚œ’„{3qwR)0/7!/O8AJ0MW@AKP-0TZ/O8;@AKPBZ+l@!/O85+7A/ K—3 K—3 63?+.-?6J,-D_,KP+07A:*]/O6*J07!/KP8E+,85j0a0ñC+.-,6cC_?/OMW:l‹3 j*3z1/O-0/79+l@!/5+ 79+.-,60:B¿V0MW/Vl+.7!Ki +-,]{…/ ä8å¥:FR‚ Ô ËÌÌOÌË å„ 3 µ035pq:,MW/OB'/O-D@!+li @AKP:-+-,6]:BC>0J*@!/7+.79]9)0KW@A/O]{@AJ07!/3¹),+.@KL8KWBC>`:7A@!+-`:7A@A/O6+._`:lV/'/O8!8A/-D@AKL+.MPMWX ‘A]{:¢KP8;J,]9)+'>0MP:.@O3 wR)0KL8qª,798Y@E/{ƒ0+B'>,MW/]{/O7;@9+.KP-0MPXZMW/O-,608E8AJ0>0>`:7A@d@!:2@!)0/-0:i @AKP:-@A),+.@E@A)0/J,8A/:.F\€DJ,+8AKiŽ79+.-,6*:`:-,/-D@AKL+.MPMWX 6*KP8;@A7!KP_0J*@A/b6Z‹EKW@A)BC/O+Œ- í7am+.-,6C@!),+l@q@A)0/]{:0MP:.@:.FS]:-*ª?60/-,]/ KW-D@!/7!Vˆ+Mx),+MF‹EKL6m@!) V/798AJ,8SÍF:7d@A),/€DJ,+0MW/j*3

−3

10

48

2

10

128

3

10

log(n)

N-,]/+.TD+.KP-az_`:.@!)¹@A)0/¢€DJ,+8AKWiŽ[:,>07A:D+]9) .+ -,6@A),/ 8Y@9+.-,60+7!6[:0>07!:0J*@!/3\wR)0/z7!/O8AJ0MW@AKP-0T2€DJ,+8AKWi [:-D@A/zpd+.7!MP:]:-*ª?60/-,]/qKP-D@A/7!Vl+.MDF:7H@!)0/R/{ƒ*>`/O] @!/O6}MW/O-0T.@!) :.F0@!)0/RMW:,+l@!)}‹R+8\jµ0Ìý¾j æ g,Ì g2`Å.É 682 “6)BMH70E3= 4Ç 2&?CfObg ýkj me,f3 pd+.7!KW:?a¢[Œ3up3+-,6 o 3½†3yz/OMP8A:-3 fbhhDk*3 [:*6*/OMi KP-0T²+.-?6‰T/-,/79+l@AKP-0T±79+.-,6*:`/O]Kª,/b6}[+.7!TKP-,+.ML8x+-,6'pq:lVl+.7!KL+.-,]/S[u+l@!7AKWƒa.+.-,6 pq)0/O8!8;_`:2þ @BAC78D o 3 ÜH3SŸMP+-0-0/7!X3ìfbhhUNV1XW2*Y!O +':)$N31?>[ZS\Q]-
25O >^ X ÜS7A/b8A8O3 _ ^J1VNV1`O >a\†pd+.B}_07AKL6*T