We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than and obeys some natural regularity conditions.
We consider excited random walks (ERWs) on ℤ with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, , is larger than 1 then ERW is transient to the right and, moreover, for >4 under the averaged measure it obeys the Central Limit Theorem. We show that when ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited random...
We consider a model of the shape of a growing polymer introduced by Durrett and Rogers ( (1992) 337–349). We prove their conjecture about the asymptotic behavior of the underlying continuous process (corresponding to the location of the end of the polymer at time ) for a particular type of repelling interaction function without compact support.
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