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Correction to: Quenched large deviation principle for words in a letter sequence
In the article Quenched large deviation principle for words in a letter sequence, Probab. Theory Relat. Fields 148, no. 3/4 (2010), 403–456 we...
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Simplifying a Proof of Transcendence for e: A Letter Exchange Between Adolf Hurwitz, David Hilbert and Paul Gordan
This article is inspired by a letter exchange between Adolf Hurwitz (1859–1919), David Hilbert (1862–1943) and Paul Gordan (1837–1912) concerning...
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Laws of large numbers
The laws of large numbers give operational meaning to the expectation of a random variable. If we generate independent realizations of a random...
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Arithmetic subtrees in large subsets of products of trees
Furstenberg-Weiss have extended Szemerédi’s theorem on arithmetic progressions to trees by showing that a large subset of the tree contains...
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GOE statistics on the moduli space of surfaces of large genus
For a compact hyperbolic surface, we define a smooth linear statistic, mimicking the number of Laplace eigenvalues in a short energy window. We study...
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Large Deviation Principle for Multi-Scale Stochastic Systems with Monotone Coefficients
The Freidlin–Wentzell’s large deviation principle is established for a class of multi-scale stochastic models involving slow–fast components, where...
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Large Deviation Principle for the Two-dimensional Stochastic Navier-Stokes Equations with Anisotropic Viscosity
In this paper we establish the large deviation principle for the the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity...
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The Global Existence of BV Solutions of the Isentropic p-System with Large Initial Data
In this paper, we study the global existence of BV solutions of the initial value problem for the isentropic p -system, where the state equation of...
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Extra-large type Artin groups are hierarchically hyperbolic
We show that Artin groups of extra-large type, and more generally Artin groups of large and hyperbolic type, are hierarchically hyperbolic. This...
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Multi-step greedy Kaczmarz algorithms with simple random sampling for solving large linear systems
By exploiting the simple random sampling and the greedy technique for capturing large residual entries, we put forth two multi-step greedy Kaczmarz...
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Upper and lower convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under large initial perturbation
We show the upper and lower bounds of convergence rates for strong solutions of the 3D non-Newtonian flows associated with Maxwell equations under a...
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Large time behavior of solutions to the critical dissipative nonlinear Schrödinger equation with large data
We consider the Cauchy problem for the dissipative nonlinear Schrödinger equation with a critical cubic nonlinearity in one space dimension. We show...
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Large deviation principle for multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motions
In this paper, we are concerned with multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motion (with...
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A Large Class of Dendrite Maps for Which Möbius Disjointness Property of Sarnak is Fulfilled
We give a simple proof that any dendrite map for which the set of endpoints is closed and countable fulfilled Sarnak Möbius disjointness. We further...
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Cubic Vertex-Transitive Graphs Admitting Automorphisms of Large Order
A connected graph of order n admitting a semiregular automorphism of order n / k is called a k -multicirculant. Highly symmetric multicirculants of...
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Invariant Measures for Large Automorphism Groups of Projective Surfaces
We classify invariant probability measures for non-elementary groups of automorphisms, on any compact Kähler surface X , under the assumption that the...
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Large Deviations and Averaging for Stochastic Tamed 3D Navier–Stokes Equations with Fast Oscillations
In this paper, we first study the strong averaging principle for stochastic tamed 3D Navier–Stokes equation with fast oscillations, which can be...
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On Chebyshev’s Theorem and Bernoulli’s Law of Large Numbers
AbstractThe law of large numbers for the case of tossing the fair coin is proven. The proof is based on the method that Chebyshev used to prove his...