Speaker: Arka Adhikari (University of Maryland)

Title: Moderate Deviations For The Capacity Of The Random Walk Range In Dimension Four

Abstract:

We find a natural four dimensional analog of the moderate deviation results for the capacity of the random walk, which corresponds to Bass, Chen and Rosen concerning the volume of the random walk range for d = 2. We find that the deviation statistics of the capacity of the random walk can be related to the following constant of generalized Gagliardo-Nirenberg inequalities,
\begin{equation*}
\inf_{f: \|\nabla f\|_{L^2}<\infty} \frac{\|f\|^{1/2}_{L^2} \|\nabla f\|^{1/2}_{L^2}}{ [\int_{(\mathbb{R}^4)^2} f^2(x) G(x-y) f^2(y) \text{d}x \text{d}y]^{1/4}}.
\end{equation*}

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Note: Back-to-back seminars with different times.