تقرير
Lower tail large deviations of the stochastic six vertex model
| العنوان: | Lower tail large deviations of the stochastic six vertex model |
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| المؤلفون: | Das, Sayan, Liao, Yuchen, Mucciconi, Matteo |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability |
| الوصف: | In this paper, we study lower tail probabilities of the height function $\mathfrak{h}(M,N)$ of the stochastic six-vertex model. We introduce a novel combinatorial approach to demonstrate that the tail probabilities $\mathbb{P}(\mathfrak{h}(M,N) \ge r)$ are log-concave in a certain weak sense. We prove further that for each $\alpha>0$ the lower tail of $-\mathfrak{h}(\lfloor \alpha N \rfloor, N)$ satisfies a Large Deviation Principle (LDP) with speed $N^2$ and a rate function $\Phi_\alpha^{(-)}$, which is given by the infimal deconvolution between a certain energy integral and a parabola. Our analysis begins with a distributional identity from BO17 [arXiv:1608.01564], which relates the lower tail of the height function, after a random shift, with a multiplicative functional of the Schur measure. Tools from potential theory allow us to extract the LDP for the shifted height function. We then use our weak log-concavity result, along with a deconvolution scheme from our earlier paper [arXiv:2307.01179], to convert the LDP for the shifted height function to the LDP for the stochastic six-vertex model height function. Comment: 35 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.08530 |
| رقم الأكسشن: | edsarx.2407.08530 |
| قاعدة البيانات: | arXiv |
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