scholarly journals Maximum weight independent sets and matchings in sparse random graphs. Exact results using the local weak convergence method

2005 ◽  
Vol 28 (1) ◽  
pp. 76-106 ◽  
Author(s):  
David Gamarnik ◽  
Tomasz Nowicki ◽  
Grzegorz Swirszcz
Keyword(s):  
Weak Convergence ◽  
Random Graphs ◽  
Independent Sets ◽  
Exact Results ◽  
Maximum Weight ◽  
Convergence Method ◽  
Local Weak Convergence ◽  
Weak Convergence Method

Large deviation principles of 2D stochastic Navier–Stokes equations with Lévy noises

2021 ◽  
pp. 1-49
Author(s):  
Huaqiao Wang
Keyword(s):  
Weak Convergence ◽  
Stokes Equations ◽  
Large Deviation ◽  
Careful Analysis ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convergence Method ◽  
Weak Convergence Method ◽  
Weak Convergence Approach

Taking the consideration of two-dimensional stochastic Navier–Stokes equations with multiplicative Lévy noises, where the noises intensities are related to the viscosity, a large deviation principle is established by using the weak convergence method skillfully, when the viscosity converges to 0. Due to the appearance of the jumps, it is difficult to close the energy estimates and obtain the desired convergence. Hence, one cannot simply use the weak convergence approach. To overcome the difficulty, one introduces special norms for new arguments and more careful analysis.

scholarly journals Large deviations for SPDEs of jump type

2015 ◽  
Vol 15 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Xue Yang ◽  
Jianliang Zhai ◽  
Tusheng Zhang
Keyword(s):  
Hilbert Space ◽  
Weak Convergence ◽  
Evolution Equation ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Random Measures ◽  
Convergence Method ◽  
Weak Convergence Method

In this paper, we establish a large deviation principle for a fully nonlinear stochastic evolution equation driven by both Brownian motions and Poisson random measures on a given Hilbert space H. The weak convergence method plays an important role.

scholarly journals Moderate deviations for stochastic models of two-dimensional second grade fluids

2018 ◽  
Vol 18 (03) ◽  
pp. 1850026 ◽  
Author(s):  
Jianliang Zhai ◽  
Tusheng Zhang ◽  
Wuting Zheng
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Weak Convergence ◽  
Stochastic Models ◽  
Moderate Deviation ◽  
Second Grade ◽  
Two Dimensional ◽  
Convergence Method ◽  
Second Grade Fluids ◽  
Weak Convergence Method

In this paper, we prove a central limit theorem and establish a moderate deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by [6] plays an important role.

scholarly journals Moderate deviations for a fractional stochastic heat equation with spatially correlated noise

2017 ◽  
Vol 17 (04) ◽  
pp. 1750025 ◽  
Author(s):  
Yumeng Li ◽  
Ran Wang ◽  
Nian Yao ◽  
Shuguang Zhang
Keyword(s):  
Heat Equation ◽  
Moderate Deviation ◽  
Stochastic Heat Equation ◽  
Correlated Noise ◽  
Derivative Operator ◽  
Spatially Correlated ◽  
Whole Space ◽  
Convergence Method ◽  
Spatially Correlated Noise ◽  
Weak Convergence Method

In this paper, we study the Moderate Deviation Principle for a perturbed stochastic heat equation in the whole space [Formula: see text]. This equation is driven by a Gaussian noise, white in time and correlated in space, and the differential operator is a fractional derivative operator. The weak convergence method plays an important role.

scholarly journals Independent Sets of Maximum Weight in Apple-Free Graphs

2010 ◽  
Vol 24 (1) ◽  
pp. 239-254 ◽  
Author(s):  
Andreas Brandstädt ◽  
Vadim V. Lozin ◽  
Raffaele Mosca
Keyword(s):  
Independent Sets ◽  
Maximum Weight

scholarly journals On independent sets in random graphs

2014 ◽  
Vol 47 (3) ◽  
pp. 436-486 ◽  
Author(s):  
Amin Coja-Oghlan ◽  
Charilaos Efthymiou
Keyword(s):  
Random Graphs ◽  
Independent Sets
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