Intermittency on catalysts: symmetric exclusion
نویسندگان
چکیده
منابع مشابه
Intermittency on catalysts : symmetric exclusion
We continue our study of intermittency for the parabolic Anderson equation ∂u/∂t = κΔu + ξu, where u : Z × [0,∞) → R, κ is the diffusion constant, Δ is the discrete Laplacian, and ξ : Z × [0,∞) → R is a space-time random medium. The solution of the equation describes the evolution of a “reactant” u under the influence of a “catalyst” ξ. In this paper we focus on the case where ξ is exclusion wi...
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The present paper provides an overview of results obtained in four recent papers by the authors. These papers address the problem of intermittency for the Parabolic Anderson Model in a time-dependent random medium, describing the evolution of a " reactant " in the presence of a " catalyst ". Three examples of catalysts are considered: (1) independent simple random walks; (2) symmetric exclusion...
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In this paper we study intermittency for the parabolic Anderson equation ∂u/∂t = κ∆u + γξu with u : Z d × [0, ∞) → R, where κ ∈ [0, ∞) is the diffusion constant, ∆ is the discrete Laplacian, γ ∈ (0, ∞) is the coupling constant, and ξ : Z d × [0, ∞) → R is a space-time random medium. The solution of this equation describes the evolution of a " reactant " u under the influence of a " catalyst " ξ...
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One form of the inclusion-exclusion principle asserts that if A and B are functions of finite sets then the formulas A(S) = ∑ T⊆S B(T ) and B(S) = ∑ T⊆S(−1) |S|−|T A(T ) are equivalent. If we replace B(S) by (−1)B(S) then these formulas take on the symmetric form A(S) = ∑ T⊆S (−1) B(T ) B(S) = ∑ T⊆S (−1) A(T ). which we call symmetric inclusion-exclusion. We study instances of symmetric inclusi...
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One form of the inclusion-exclusion principle asserts that if A and B are functions of finite sets then the formulas A(S) = ∑ T⊆S B(T ) and B(S) = ∑ T⊆S(−1) |A(T ) are equivalent. If we replace B(S) by (−1)|S|B(S) then these formulas take on the symmetric form A(S) = ∑
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2007
ISSN: 1083-6489
DOI: 10.1214/ejp.v12-407