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Abstract We investigate the low moments$$\mathbb {E}[|A_N|^{2q}],\, 0 $E\left[\right|A_N{|}^{2q}],0<q⩽1$of secular coefficients$$A_N$$ $A_N$of the critical non-Gaussian holomorphic multiplicative chaos, i.e. coefficients of$$z^N$$ $z^N$in the power series expansion of$$\exp (\sum _{k=1}^\infty X_kz^k/\sqrt{k})$$ $exp({\sum }_{k=1}^{\infty }{X}_k{z}^k/\sqrt{k})$, where$$\{X_k\}_{k\geqslant 1}$$ ${\left\{X_k\right\}}_{k⩾1}$are i.i.d. rotationally invariant unit variance complex random variables. Inspired by Harper’s remarkable result on random multiplicative functions, Soundararajan and Zaman recently showed that if each$$X_k$$ $X_k$is standard complex Gaussian,$$A_N$$ $A_N$features better-than-square-root cancellation:$$\mathbb {E}[|A_N|^2]=1$$ $E\left[\right|A_N{|}^2]=1$and$$\mathbb {E}[|A_N|^{2q}]\asymp (\log N)^{-q/2}$$ $E\left[\right|A_N{|}^{2q}]\asymp {(logN)}^{-q/2}$for fixed$$q\in (0,1)$$ $q\in (0,1)$as$$N\rightarrow \infty $$ $N\to \infty$. We show that this asymptotics holds universally if$$\mathbb {E}[e^{\gamma |X_k|}]<\infty $$ $E\left[e^{\gamma |X_k|}\right]<\infty$for some$$\gamma >2q$$ $\gamma >2q$. As a consequence, we establish the universality for the tightness of the normalized secular coefficients$$A_N(\log (1+N))^{1/4}$$ $A_N{(log(1+N))}^{1/4}$, generalizing a result of Najnudel, Paquette, and Simm. Another corollary is the almost sure regularity of some critical non-Gaussian holomorphic chaos in appropriate Sobolev spaces. Moreover, we characterize the asymptotics of$$\mathbb {E}[|A_N|^{2q}]$$ $E\left[\right|A_N{|}^{2q}]$for$$|X_k|$$ $|X_k|$following a stretched exponential distribution with an arbitrary scale parameter, which exhibits a completely different behavior and underlying mechanism from the Gaussian universality regime. As a result, we unveil a double-layer phase transition around the critical case of exponential tails. Our proofs combine Harper’s robust approach with a careful analysis of the (possibly random) leading terms in the monomial decomposition of$$A_N$$ $A_N$. 

Abstract The first experimental realization of the intrinsic (not dominated by defects) charge conduction regime in lead‐halide perovskite field‐effect transistors (FETs) is reported. The advance is enabled by: i) a new vapor‐phase epitaxy technique that results in large‐area single‐crystalline cesium lead bromide (CsPbBr₃) films with excellent structural and surface properties, including atomically flat surface morphology, essentially free from defects and traps at the level relevant to device operation; ii) an extensive materials analysis of these films using a variety of thin‐film and surface probes certifying the chemical and structural quality of the material; and iii) the fabrication of nearly ideal (trap‐free) FETs with characteristics superior to any reported to date. These devices allow the investigation of the intrinsic FET and (gated) Hall‐effect carrier mobilities as functions of temperature. The intrinsic mobility is found to increase on cooling from ≈30 cm²V⁻¹s⁻¹at room temperature to ≈250 cm²V⁻¹s⁻¹at 50 K, revealing a band transport limited by phonon scattering. Establishing the intrinsic (phonon‐limited) mobility provides a solid test for theoretical descriptions of carrier transport in perovskites, reveals basic limits to the technology, and points to a path for future high‐performance perovskite electronic devices.