Coalescence and total-variation distance of semi-infinite inverse-gamma polymers

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Firas Rassoul-Agha, Timo Seppäläinen, Xiao Shen
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引用次数: 0

Abstract

We show that two semi-infinite positive temperature polymers coalesce on the scale predicted by KPZ (Kardar–Parisi–Zhang) universality. The two polymer paths have the same asymptotic direction and evolve in the same environment, independently until coalescence. If they start at distance k $k$ apart, their coalescence occurs on the scale k 3 / 2 $k^{3/2}$ . It follows that the total variation distance of two semi-infinite polymer measures decays on this same scale. Our results are upper and lower bounds on probabilities and expectations that match, up to constant factors and occasional logarithmic corrections. Our proofs are done in the context of the solvable inverse-gamma polymer model, but without appeal to integrable probability. With minor modifications, our proofs give also bounds on transversal fluctuations of the polymer path. As the free energy of a directed polymer is a discretization of a stochastically forced viscous Hamilton–Jacobi equation, our results suggest that the hyperbolicity phenomenon of such equations obeys the KPZ exponent.

半无限反伽马聚合物的凝聚和总变距离
我们的研究表明,两种半无限正温聚合物在 KPZ(卡达尔-帕里什-张)普遍性预测的尺度上凝聚。这两种聚合物的路径具有相同的渐近方向,并在相同的环境中独立演化,直至凝聚。如果它们的起始距离为 k $k$,那么它们的凝聚发生在尺度为 k 3 / 2 $k^{3/2}$ 的范围内。由此可见,两个半无限聚合物测量的总变异距离也是在这个尺度上衰减的。我们的结果是概率的上界和下界,以及与之相匹配的期望值,最多不超过常数因子和偶尔的对数修正。我们的证明是在可解逆伽马高分子模型的背景下完成的,但没有诉诸可积分概率。稍作修改后,我们的证明还给出了聚合物路径横向波动的边界。由于定向聚合物的自由能是随机强迫粘性汉密尔顿-贾可比方程的离散化,我们的结果表明,此类方程的双曲现象服从 KPZ 指数。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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