Multiplicative coherent systems of distributions-on the Young graph

Rozhkovskaya, Natasha

doi:10.1007/bf02175836

Cited by 6 publications

(12 citation statements)

References 3 publications

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“…The measures {Å α n } on the Schur graph do not have a representation-theoretic interpretation in the spirit of [KOV93], [KOV04] yet. However, combinatorially they look very similar to the z-measures: the families M z,z ′ n and Å α n can be characterized in a unified manner, see [Roz99], [Bor99]; see also [Pet10c, §4.1] for another characterization. On the other hand, most results about Å α n do not follow directly from the corresponding results about the z-measures.…”

Section: The Problem Of Harmonic Analysis On the Infinite Symmetric G...mentioning

confidence: 99%

“…Both families of measures that we consider can be interpreted through certain specializations of Schur symmetric functions s τ , τ ∈ From the above two formulas one sees that the weights {Å α n (λ)} λ∈Ën are proportional (with a coefficient depending only on n) to square roots of the weights {M z(α),z ′ (α) 2n (Dλ)} λ∈Ën . (Alternatively, this can be seen from §5 and the multiplicative nature of our measures [Roz99], [Bor99].) This property can easily be reformulated in probabilistic terms, but it does not seem to provide a direct way of obtaining properties of Å α n from the corresponding properties of the z-measures.…”

Section: Schur Measures and An Analogue For Shifted Diagramsmentioning

confidence: 99%

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On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group

Petrov¹

2011

Preprint

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The z-measures on partitions originated from the problem of harmonic analysis of linear representations of the infinite symmetric group in the works of Kerov, Olshanski and Vershik [KOV93], [KOV04]. A similar family corresponding to projective representations was introduced by Borodin [Bor99]. The latter measures live on strict partitions (i.e., partitions with distinct parts), and the z-measures are supported by all partitions. In this note we describe some combinatorial relations between these two families of measures using the well-known doubling of shifted Young diagrams.

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Section: The Problem Of Harmonic Analysis On the Infinite Symmetric G...mentioning

confidence: 99%

Section: Schur Measures and An Analogue For Shifted Diagramsmentioning

confidence: 99%

On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group

Petrov¹

2011

Preprint

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“…This allows one to give a purely combinatorial characterization of the z-measures on the Young graph. Another characterization of the z-measures similar to Theorem 3.4 (of [Bor99]) is given in [Roz99].…”

Section: Kerov's Operatorsmentioning

confidence: 99%

Pfaffian Stochastic Dynamics of Strict Partitions

Petrov

2011

Electron. J. Probab.

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We study a family of continuous time Markov jump processes on strict partitions (partitions with distinct parts) preserving the distributions introduced by Borodin [Bor99] in connection with projective representations of the infinite symmetric group. The one-dimensional distributions of the processes (i.e., the Borodin's measures) have determinantal structure. We express the dynamical correlation functions of the processes in terms of certain Pfaffians and give explicit formulas for both the static and dynamical correlation kernels using the Gauss hypergeometric function. Moreover, we are able to express our correlation kernels (both static and dynamical) through those of the z-measures on partitions obtained previously by Borodin and Olshanski in a series of papers.The results about the fixed time case were announced in the note [Pet10a]. A part of the present paper contains proofs of those results.

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“…The z-measures first appeared from a representation-theoretic construction of generalized regular representations of S(∞). Then a couple of algebraic/combinatorial characterizations of these measures were suggested in [Roz99] and [BO00b]. In the latter paper another graphs were also studied.…”

Section: Introductionmentioning

confidence: 99%

$\mathfrak{sl}(2)$ operators and Markov processes on branching graphs

Petrov

2013

J Algebr Comb

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Let Γ be a graph and P be a reversible random walk on Γ. From the L 2 analyticity of the Markov operator P , we deduce that an iterate of odd exponent of P is 'lazy', that is there exists an integer k such that the transition probability (for the random walk P 2k+1) from a vertex x to itself is uniformly bounded from below. The proof does not require the doubling property on Γ but only a polynomial control of the volume.

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Multiplicative coherent systems of distributions-on the Young graph

Cited by 6 publications

References 3 publications

On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group

On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group

Pfaffian Stochastic Dynamics of Strict Partitions

$\mathfrak{sl}(2)$ operators and Markov processes on branching graphs

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