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Long-term behavior of stochastic models on lattices with spatio-temporal interactions

具有时空相互作用的格子上随机模型的长期行为

基本信息

批准号：
22K03333
负责人：
竹居正登
金额：
$ 2.33万
依托单位：
Yokohama National University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2022
资助国家：
日本
起止时间：
2022-04-01 至 2026-03-31
项目状态：
未结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22K03333/
关键词：
ランダムウォークパーコレーション極限定理格子確率モデル

项目摘要

研究計画に従って時間的・空間的に相互作用をもつ確率モデルの研究を進めた．その結果，(1) ファーストパッセージパーコレーション問題における極限定理，(2) 記憶のあるランダムウォークに対する極限定理，(3) 記憶のあるランダムウォークの極限定理を応用した至る所微分不可能な連続関数の性質の研究について新たな知見を蓄積することができた．特に，(2)のテーマについて得られた成果について述べる．Elephant random walk with stopsは，"step-reinforcement"と呼ばれる仕組みにより推移確率が変動する離散時間ランダムウォークであり，左右の隣接点に移動する他，その場で留まることも許したものである．「その場で留まる」確率rを固定したときに，記憶と同じ向きに進む度合いを表すもうひとつのパラメータpに応じて3つの異なる相が生じるが，r>0の場合，r=0である通常のelephant random walkとは量的にも質的にも異なる極限挙動を示すことがBercu (2022)等によって示されている．横浜国立大学の秋元達哉氏・谷口恵祐氏と共同で，r>0の場合の長時間挙動を記述する極限定理について研究した．時刻nまでに訪問した点の総数の増大度について研究し，r,pに応じて多様な挙動が生じることを示した．また，r>0の場合に時刻nまでにウォーカーが移動した回数と時刻nでのウォーカーの位置の相関係数について調べ，ある種の特別な状況を除いてはpに応じてn→∞での挙動に3つの異なる様相が見られることを証明した．この成果を論文としてとりまとめているところである．

In the study of the interaction between space and time, the accuracy rate is improved. The results are as follows: (1) do not know how to solve the problem of health problems, and (2) record the limit theorem of health problems. (3) to record the limit theorem of the number of links that are not possible by using the theory of limit. (3) to learn that it is not possible to change the number of data. (3) to record the limit theorem of the limit theorem. (3) record the limit theorem of the limit theorem of the number of data that is not possible. The "step-reinforcement" system calls on the staff to make sure that the rate of movement is increased, the time for the movement of the train is changed, the contact on the left and the right is moved, and the contact on the left and the right is moved, and the number of employees is retained. Record the same level of progress in the same way as in the same way as in the same table. This is the same as that in the table. This is the same as that in the same table. This is the same as the progress in the table. This is the same as the progress in the table. This is the same as that in the table. This is the same as the progress in the same direction. This is the same as the progress in the table. This is the same as that in r&gt. At the end of the day, there is a general limit on the number of elephant random walk tickets, such as Bercu (2022). Yokohama National University, Taniguchi, Yokohama 0: 00 hours of long-term activity record limit Theorem for the study of tracks. at the moment, the number of points is much larger than that of the study, and the number of points is much larger than that of the study. at the same time, the number of points is much higher than that in the study of the number of points, and the number of points. At the end of the day, you need to change the number of calls. when you are in the same time as you are in the same position, you need to know that you are in the same position as you are in the same time as you are in the same time as you are in the same situation.