rapport

V={1, . . . n}
p, 0< p < 1p
Gp

pk=n
kpk(1 −p)n−k
z=E(k) = p∗(n−1)
n m =m(n)Gm
n m (n
2)
m−1
Gm
n
Q p
Q
n
p=m/n
2

G0(x)
G0(x) =
∞
X
k=0
pkxk
pkk
G0G0(1) = 1 G(pk)
z=X
k
k∗pk=G0
0(1)
X
X m
m
[G0(x)]2="X
k
pk∗xk#
=X
j,k
pk∗pj∗xj+k

xnpj∗pkj+k=n
n
GpGm
k pk=
n
kpk(1 −p)n−k
Ωnqn
QΩnQ
limn7→∞ qn= 1
p Gp
2
X(Gp)
Gp2X=Pi,j∈[1...n]2Xi,j Xi,j = 1
vi, vji0, j0Xi0,j0= 1
n−2i0j0P[Xi,j = 1] =
(1 −p2)n−2E(X) = n
2∗(1 −p2)n−2
p E(X)7→ 0
P(X= 0) 7→ 1Gp2
p
p
p2∗n−2∗log n7→ ∞ n2(1 −p)7→ ∞ Gp
2
M=M(n)<n
22∗M2
n3−log n7→ ∞
GM2
X E(X) = `n
2´∗p(n)

Q
t(n)p(n)/t(n)7→ 0Gp
Q p(n)/t(n)7→ ∞ GpQ
t:n7→ ln(n)/n
z1=< k >=X
k
k∗pk=G0
0(1)
n
n0k
k∗pk
G1(x) = Pkk∗pk∗xk−1
Pkk∗pk
=1
< k >G0
0(x)
z1=< k >=G0
0
zmm
zm= [G0(1)]m−1G0
0(1) = z2
z1m−1
D
1 +
t
X
m=1
zm=n
l=ln(n/z1)
ln(z2/z1)+ 1
l < k >l< k >l=n
l∝ln(n)
ln(< k >)