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KAKEN_23740086seika.pdf
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Download
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:87.9 KB
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確率界面モデルの漸近挙動の研究
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カクリツ カイメン モデル ノ ゼンキン キョドウ ノ ケンキュウ
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Kakuritsu kaimen moderu no zenkin kyodo no kenkyu
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Study on asymptotic behavior of stochastic interface models
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坂川, 博宣
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サカガワ, ヒロノブ
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Sakagawa, Hironobu
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慶應義塾大学・理工学部・講師
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Research team head
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科研費研究者番号 : 60348810
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2014
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科学研究費補助金研究成果報告書
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2013
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本研究では相分離界面や細胞膜などの数学的な解析を目指し, 対応するいくつかの格子上の確率モデルを取り上げその漸近挙動に関する研究を行った。具体的には細胞膜の確率モデルの１つであるΔφモデルにおいて２つの種類の自己ポテンシャルを加えた場合における系の自由エネルギーの挙動を調べた。また∇φ界面モデルの時間発展において原点に着目した場合に現れるGauss過程に対し持続確率の漸近挙動に関する評価を行った。
In this research, we considered several stochastic models on lattice and studied its asymptotic behavior for the mathematical analysis of phase separating interface and membrane. We first considered Laplacian phi model as a model of membrane and studied its free energy under the effect of two types of external potentials. We also considered a Gaussian process which appears in the time evolution of gradient phi interface model and obtained estimates on its persistence probability.
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研究種目 : 若手研究(B)
研究期間 : 2011～2013
課題番号 : 23740086
研究分野 : 数物系科学
科研費の分科・細目 : 数学・数学一般(含確率論・統計数学)
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