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Regular version of the site
Of all publications in the section: 4
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Article
Sergeev A. Science China Mathematics. 2008. Vol. 51. No. 4. P. 695-706.
Added: Feb 19, 2013
Article
Cranston M., Molchanov S. Science China Mathematics. 2019. Vol. 62. No. 8. P. 1463-1476.

We begin with the reference measure P0 induced by simple, symmetric nearest neighbor continuous time random walk on Zd starting at 0 with jump rate 2d and then define, for β ⩾ 0, t > 0, the Gibbs probability measure Pβ,t by specifying its density with respect to P0 as dPβ,tdP0=Zβ,t(0)−1eβ∫t0δ0(xs)ds,dPβ,tdP0=Zβ,t(0)−1eβ∫0tδ0(xs)ds, (0.1) where Zβ,t(0)≡E0[eβ∫t0δ0(xs)ds].Zβ,t(0)≡E0[eβ∫0tδ0(xs)ds].. This Gibbs probability measure provides a simple model for a homopolymer with an attractive potential at the origin. In a previous paper (Cranston and Molchanov, 2007), we showed that for dimensions d ⩾ 3 there is a phase transition in the behavior of these paths from the diffusive behavior for β below a critical parameter to the positive recurrent behavior for β above this critical value. The critical value was determined by means of the spectral properties of the operator Δ + βδ0, where Δ is the discrete Laplacian on Zd. This corresponds to a transition from a diffusive or stretched-out phase to a globular phase for the polymer. In this paper we give a description of the polymer at the critical value where the phase transition takes place. The behavior at the critical parameter is dimension-dependent.

Added: Nov 14, 2019
Article
Blokh A., Oversteegen L., Timorin V. Science China Mathematics. 2018. Vol. 61. No. 12. P. 2121-2138.
Added: Nov 24, 2018
Article
Bohning C., Graf von Bothmer H., Bogomolov F. A. Science China Mathematics. 2011. Vol. 54. No. 8. P. 1521-1532.
Added: Jun 20, 2011