Moments of Partition Functions of 2d Gaussian Polymers in the Weak Disorder Regime-I
Let W N ( β ) = E 0 e ∑ n = 1 N β ω ( n , S n ) - N β 2 / 2 be the partition function of a two-dimensional directed polymer in a random environment, where ω ( i , x ) , i ∈ N , x ∈ Z 2 are i.i.d. standard normal and { S n } is the path of a random walk. With β = β N = β ^ π / log N and β ^ ∈ ( 0 , 1...
Saved in:
| Published in: | Communications in mathematical physics Vol. 403; no. 1; pp. 417 - 450 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2023
Springer Nature B.V Springer Verlag |
| Subjects: | |
| ISSN: | 0010-3616, 1432-0916 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let
W
N
(
β
)
=
E
0
e
∑
n
=
1
N
β
ω
(
n
,
S
n
)
-
N
β
2
/
2
be the partition function of a two-dimensional directed polymer in a random environment, where
ω
(
i
,
x
)
,
i
∈
N
,
x
∈
Z
2
are i.i.d. standard normal and
{
S
n
}
is the path of a random walk. With
β
=
β
N
=
β
^
π
/
log
N
and
β
^
∈
(
0
,
1
)
(the subcritical window),
log
W
N
(
β
N
)
is known to converge in distribution to a Gaussian law of mean
-
λ
2
/
2
and variance
λ
2
, with
λ
2
=
log
(
1
/
(
1
-
β
^
2
)
)
(Caravenna et al. in Ann Appl Probab 27(5):3050–3112, 2017). We study in this paper the moments
E
[
W
N
(
β
N
)
q
]
in the subcritical window, for
q
=
O
(
log
N
)
. The analysis is based on ruling out triple intersections. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0010-3616 1432-0916 |
| DOI: | 10.1007/s00220-023-04799-2 |