We study the fluctuations in equilibrium of a class of Brownian motions interacting through a potential. For a certain choice of exponential potential, the distribution of the system coincides with differences of free energies of the stationary semi-discrete or O'Connell-Yor polymer.We show that for Gaussian potentials, the fluctuations are of order N 1 4 when the time and system size coincide, whereas for a class of more general convex potentials V the fluctuations are of order at most N 1 3 . In the O'Connell-Yor case, we recover the known upper bounds for the fluctuation exponents using a dynamical approach, without reference to the polymer partition function interpretation.
This chapter examines the rationale, the institutional set-up and the practice of Russia’s language promotion and puts it into perspective by juxtaposing it to British, French and German practices. How do the aims of Russian cultural diplomacy, in terms of “influencing” and “mediating” compare to those of the Western European States? In how far is the institutional set-up of the Russkii Mir Foundation and of the state agency Rossotrudnichestvo and their relationship to educational and foreign ministries comparable to those of the British Council, the Alliance Française and the Goethe Institutes? Which methods of language promotion do these organisations offer to prospective students? Finally, the chapter compares Russia’s contemporary language and culture promotion with the history of Soviet cultural diplomacy and discusses whether or not Russia’s soft power initiative is more than old wine in new bottles.
In this paper, we consider four integrable models of directed polymers for which the free energy is known to exhibit KPZ fluctuations. A common framework for the analysis of these models was introduced in [14].We derive estimates for the central moments of the partition function, of any order, on the near-optimal scale N 1{3`ǫ , using the iterative method we applied to the semi-discrete polymer in [9]. Among the innovations exploiting the invariant structure, we develop formulas for correlations between functions of the free energy and the boundary weights that replace the Gaussian integration by parts appearing in our previous paper [9].
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