2007年3月
Moment Problem in Replica Method
Interdisciplinary Information Sciences
- 巻
- 13
- 号
- 1
- 開始ページ
- 17
- 終了ページ
- 23
- 記述言語
- 英語
- 掲載種別
- DOI
- 10.4036/iis.2007.17
- 出版者・発行元
- 東北大学
The main objective of this paper is to discuss mathematical validity of the replica method. We focus on the observation that the replica method calculates {\Bbb E}(logZ) from the moment sequence {\Bbb E}(Zn)} of a positive random variable Z, or equivalently, it calculates expectation {\Bbb E}(X) of a random variable X on the basis of its moment generating function \overline{\varphi}(u)={\Bbb E}(euX) while evaluating \overline{\varphi}(u) only at positive integers u=1,2,…. This aspect of the replica method will be justified if the moment problem is solved affirmatively. In this paper, we provide some counterexamples for each of which the moment sequence of Z does not uniquely determine {\Bbb E}(logZ), thereby invalidating unconditional justification of the replica method.
- リンク情報
- ID情報
-
- DOI : 10.4036/iis.2007.17
- ISSN : 1340-9050
- CiNii Articles ID : 110006271960
- CiNii Books ID : AA11032627