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Seibergwitten theory and random partitions
"... We study N = 2 supersymmetric four dimensional gauge theories, in a certain N = 2 supergravity background, called Ωbackground. The partition function of the theory in the Ωbackground can be calculated explicitly. We investigate various representations for this partition function: a statistical sum ..."
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Cited by 267 (9 self)
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sum over random partitions, a partition function of the ensemble of random curves, a free fermion correlator. These representations allow to derive rigorously the SeibergWitten geometry, the curves, the differentials, and the prepotential. We study pure N = 2 theory, as well as the theory with matter
Infinite wedge and random partitions
 Selecta Mathematica (new series
"... The aim of this paper is to show that random partitions have a very natural and direct connection to various structures which are well known in integrable systems. This connection is arguably even more natural than, for example, ..."
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Cited by 95 (6 self)
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The aim of this paper is to show that random partitions have a very natural and direct connection to various structures which are well known in integrable systems. This connection is arguably even more natural than, for example,
The uses of random partitions
"... These are extended notes for my talk at the ICMP 2003 in Lisbon. Our goal here is to demonstrate how natural and fundamental random partitions are from many different points of view. We discuss various natural measures on partitions, their correlation functions, limit shapes, and how they arise in a ..."
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Cited by 30 (3 self)
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These are extended notes for my talk at the ICMP 2003 in Lisbon. Our goal here is to demonstrate how natural and fundamental random partitions are from many different points of view. We discuss various natural measures on partitions, their correlation functions, limit shapes, and how they arise
Random partitions and instanton counting
 Proceedings of the international congress of mathematicians (ICM
"... Abstract. We summarize the connection between random partitions and N = 2 supersymmetric gauge theories in 4 dimensions and indicate how this relation extends to higher dimensions. Mathematics Subject Classification (2000). Primary 81T13; Secondary 14J60. 1. ..."
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Cited by 5 (1 self)
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Abstract. We summarize the connection between random partitions and N = 2 supersymmetric gauge theories in 4 dimensions and indicate how this relation extends to higher dimensions. Mathematics Subject Classification (2000). Primary 81T13; Secondary 14J60. 1.
Increments of Random Partitions
, 2008
"... For any partition of {1, 2,..., n} we define its increments Xi,1 ≤ i ≤ n by Xi = 1 if i is the smallest element in the partition block that contains it, Xi = 0 otherwise. We prove that for partially exchangeable random partitions (where the probability of a partition depends only on its block sizes ..."
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For any partition of {1, 2,..., n} we define its increments Xi,1 ≤ i ≤ n by Xi = 1 if i is the smallest element in the partition block that contains it, Xi = 0 otherwise. We prove that for partially exchangeable random partitions (where the probability of a partition depends only on its block sizes
Increments of Random Partitions
, 2008
"... For any partition of {1, 2,..., n} we define its increments Xi,1 ≤ i ≤ n by Xi = 1 if i is the smallest element in the partition block that contains it, Xi = 0 otherwise. We prove that for partially exchangeable random partitions (where the probability of a partition depends only on its block sizes ..."
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For any partition of {1, 2,..., n} we define its increments Xi,1 ≤ i ≤ n by Xi = 1 if i is the smallest element in the partition block that contains it, Xi = 0 otherwise. We prove that for partially exchangeable random partitions (where the probability of a partition depends only on its block sizes
Asymptotic analysis of random partitions
"... In this paper we aim to review some works on the asymptotic behaviors of random partitions. The focus is upon two basic probability models — uniform partitions and Plancherel partitions. One of fundamental results is the existence of limit shapes, which corresponds to the classic law of large numbe ..."
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In this paper we aim to review some works on the asymptotic behaviors of random partitions. The focus is upon two basic probability models — uniform partitions and Plancherel partitions. One of fundamental results is the existence of limit shapes, which corresponds to the classic law of large
Gaussian fluctuations for random partitions
"... A partition λ of an integer number n ≥ 1 is any integer sequence λ = (λ1, λ2,...) such that λ1 ≥ λ2 ≥ · · · ≥ 0 and n = λ1 + λ2 + · · · (notation: λ ⊢ n). In particular, λ1 = max{λi ∈ λ}. The standard geometric object associated to the partition λ ⊢ n is its Young diagram consisting of n unit ..."
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A partition λ of an integer number n ≥ 1 is any integer sequence λ = (λ1, λ2,...) such that λ1 ≥ λ2 ≥ · · · ≥ 0 and n = λ1 + λ2 + · · · (notation: λ ⊢ n). In particular, λ1 = max{λi ∈ λ}. The standard geometric object associated to the partition λ ⊢ n is its Young diagram consisting of n unit
Results 1  10
of
3,072