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...s. Although our main results are about the free energy, the core of our approach is a precise pathwise description of the field based on Markov renewal theory. In analogy to [10, 9] and especially to =-=[8]-=-, we would like to stress the power of (Markov) renewal theory techniques for the study of (1 + 1)–dimensional linear chain models. The other basic techniques that we use are local limit theorems and ...

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...6]. Moreover, from a more strictly mathematical viewpoint, the close link between pinning models and renewal theory is another matter of interest since non-trivial cross-questions arise (we cite e.g. =-=[11]-=- and [20], but the present work in itself is heavily based on the interplay with renewal theory). Pinning models are indexed by a positive parameter that we call α (in agreement with the probabilistic...

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.... A. Bryn-Jones and R. A. Doney, Manchester University 1. Introduction There is an increasing use in modelling of processes derived from random walks which are constrained to stay on a half-line; see =-=[10]-=- for a recent example of this. However the phrase "random walk conditioned to stay non-negative" has at least two di¤erent interpretations. In the …rst we consider the …rst n values of a random walk c...

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... model, known as inhomogeneous pinning model, has been studied in depth in the literature (see [15, 16] for complete reviews on the subject), in particular in the cases where ω is a periodic sequence =-=[9, 10, 11]-=- and where ω is a typical realization of a sequence of i.i.d. variables [1, 3, 12, 17, 19, 20]. In this paper, we focus on a particular type of environment ω, constructed as follows: Let τ̂ = (τ̂n)n >...

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...termssINFINITE VOLUME LIMITS OF PERIODIC POLYMER CHAINS 5 of the charges ω, see Theorem 2.1 below, that has been first derived in [6], by means of large deviations techniques, and then re–obtained in =-=[8]-=-, using a more direct approach based on renewal theory. One of the purposes of this work is to present (in Section 2) a direct self-contained proof of this formula, using renewal theory ideas in analo...

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...use of this kind of techniques in the field of polymer models has proved to be extremely successful, starting from [8] and [4], and has been generalized more recently to cover Markovian settings, cf. =-=[3]-=- and [2]. The key point is to get sharp estimates on suitable renewal functions. Although the same approach can be applied also to the case δ < 0, i.e., when touching an interface entails a penalty, r...

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...t of (1+1)–dimensional random walk models for polymer chains and interfaces. We look in particular at the copolymer near a selective interface model, both in the disordered [3, 1] and in the periodic =-=[4, 5]-=- setting, but also at the interface wetting models considered in [7, 6] and at pinning models based on random walks, described e.g. in [9] (to which we refer for a detailed overview on all these model...

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... kinds of techniques in the field of polymer models has proven to be extremely successful, starting from [4] and [9], and, more recently, has been generalized to cover Markovian settings; see [2] and =-=[5]-=-. The key point is to get sharp estimates on suitable renewal functions. The same approach can be applied to deal with the depinning case δ < 0, that is, when touching an interface entails a penalty r...

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...tem at the annealed critical curve is equivalent to the pinning of a Markov renewal process. We mention that such tools were previously used in the study of pinning with periodic inhomogeneities (see =-=[5]-=-; indeed, our model includes periodic sequences). As noticed in the previous subsection, the annealed critical curve provides a lower bound on hc(β), but the issue of disorder (ir)relevance is open. 1...