ترغب بنشر مسار تعليمي؟ اضغط هنا

On large deviation rate functions for a continuous-time directed polymer in weak disorder

56   0   0.0 ( 0 )
 نشر من قبل Ryoki Fukushima
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We show that the endpoint large deviation rate function for a continuous-time directed polymer agrees with the rate function of the underlying random walk near the origin in the whole weak disorder phase.



قيم البحث

اقرأ أيضاً

We derive properties of the rate function in Varadhans (annealed) large deviation principle for multidimensional, ballistic random walk in random environment, in a certain neighborhood of the zero set of the rate function. Our approach relates the LD P to that of regeneration times and distances. The analysis of the latter is possible due to the i.i.d. structure of regenerations.
88 - Xiaobin Sun , Ran Wang , Lihu Xu 2018
A Freidlin-Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and the fast co mponent is a stochastic reaction-diffusion equation. Our approach is via the weak convergence criterion developed in [3].
84 - Takuya Saito 2013
We discuss temporal efficiency of template-directed polymer synthesis, such as DNA replication and transcription, under a given template string. To weigh the synthesis speed and accuracy on the same scale, we propose a template-directed synthesis (TD S) rate, which contains an expression analogous to that for the Shannon entropy. Increasing the synthesis speed accelerates the TDS rate, but the TDS rate is lowered if the produced sequences are diversified. We apply the TDS rate to some production system models and investigate how the balance between the speed and the accuracy is affected by changes in the system conditions.
In this paper, we consider four integrable models of directed polymers for which the free energy is known to exhibit KPZ fluctuations. A common framework for the analysis of these models was introduced in our recent work on the OConnell-Yor polymer. We derive estimates for the central moments of the partition function, of any order, on the near-optimal scale $N^{1/3+epsilon}$, using an iterative method. Among the innovations exploiting the invariant structure, we develop formulas for correlations between functions of the free energy and the boundary weights that replace the Gaussian integration by parts appearing in the analysis of the OConnell-Yor case.
We initiate a study of large deviations for block model random graphs in the dense regime. Following Chatterjee-Varadhan(2011), we establish an LDP for dense block models, viewed as random graphons. As an application of our result, we study upper tai l large deviations for homomorphism densities of regular graphs. We identify the existence of a symmetric phase, where the graph, conditioned on the rare event, looks like a block model with the same block sizes as the generating graphon. In specific examples, we also identify the existence of a symmetry breaking regime, where the conditional structure is not a block model with compatible dimensions. This identifies a reentrant phase transition phenomenon for this problem---analogous to one established for Erdos-Renyi random graphs (Chatterjee-Dey(2010), Chatterjee-Varadhan(2011)). Finally, extending the analysis of Lubetzky-Zhao(2015), we identify the precise boundary between the symmetry and symmetry breaking regime for homomorphism densities of regular graphs and the operator norm on Erdos-Renyi bipartite graphs.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا