From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction

Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph $G$ and the dimer model defined on a decorated version \GD of this graph \cite{Fisher}. In this paper we explicitly relate the dimer model associated to the critical Ising model and critical cycle rooted spanning forests (CRSFs). This relation is established through characteristic polynomials, whose definition only depends on the respective fundamental domains, and which encode the combinatorics of the model. We first show a matrix-tree type theorem establishing that the dimer characteristic polynomial counts CRSFs of the decorated fundamental domain \GD_1. Our main result consists in explicitly constructing CRSFs of \GD_1 counted by the dimer characteristic polynomial, from CRSFs of $G_1$ where edges are assigned Kenyon's critical weight function \cite{Kenyon3}; thus proving a relation on the level of configurations between two well known 2-dimensional critical models.Comment: 51 pages, 24 figures. To appear, Comm. Math. Phys. Revised version: title has changed. The terminology `correspondence' has been changed to that of `explicit construction' and `mapping

Scaling limits of random skew plane partitions with arbitrarily sloped back walls

The paper studies scaling limits of random skew plane partitions confined to a box when the inner shapes converge uniformly to a piecewise linear function V of arbitrary slopes in [-1,1]. It is shown that the correlation kernels in the bulk are given by the incomplete Beta kernel, as expected. As a consequence it is established that the local correlation functions in the scaling limit do not depend on the particular sequence of discrete inner shapes that converge to V. A detailed analysis of the correlation kernels at the top of the limit shape and of the frozen boundary is given. It is shown that depending on the slope of the linear section of the back wall, the system exhibits behavior observed in either [OR2] or [BMRT].Comment: 29 pages. Version 2: Several sections and proofs were improved and completely rewritten. These include Sections 2.2.2,2.2.4 and 2.2.5, Lemmas 2.3 and 4.2, and Proposition 4.1. Section 1.1.3 was added. This version is to be published in Comm. Math. Phy

Évolution du taux d’intermédiation financière en France (1994-2004).

Taux d’intermédiation financière, agrégats d’intermédiation, marchés de capitaux/financements de marché, crédits/financements immobiliers, intermédiaires financiers, internationalisation/diversification géographique des placements, non-résidents, tarification/revenus d’intermédiation, services d’intermédiation financière indirectement mesurés (SIFIM), production des institutions financières.

Random skew plane partitions with a piecewise periodic back wall

Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis is fairly similar to that in [OR2], but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic) curve, whereas the boundary in [OR2] is singular. We also observe the bead process introduced in [B] appearing in the asymptotics at the top of the limit shape.Comment: 24 pages. This version to appear in Annales Henri Poincar

Local Statistics of Realizable Vertex Models

We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, and 1-2 model, which we will define. We express the local statistics of a large class of vertex models on a finite hexagonal lattice as a linear combination of the local statistics of dimers on the corresponding Fisher graph, with the help of a generalized holographic algorithm. Using an $n\times n$ torus to approximate the periodic infinite graph, we give an explicit integral formula for the free energy and local statistics for configurations of the vertex model on an infinite bi-periodic graph. As an example, we simulate the 1-2 model by the technique of Glauber dynamics

Dynamics of Shock Probes in Driven Diffusive Systems

We study the dynamics of shock-tracking probe particles in driven diffusive systems and also in equilibrium systems. In a driven system, they induce a diverging timescale that marks the crossover between a passive scalar regime at early times and a diffusive regime at late times; a scaling form characterises this crossover. Introduction of probes into an equilibrium system gives rise to a system-wide density gradient, and the presence of even a single probe can be felt across the entire system.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen

The critical Ising model via Kac-Ward matrices

The Kac-Ward formula allows to compute the Ising partition function on any finite graph G from the determinant of 2^{2g} matrices, where g is the genus of a surface in which G embeds. We show that in the case of isoradially embedded graphs with critical weights, these determinants have quite remarkable properties. First of all, they satisfy some generalized Kramers-Wannier duality: there is an explicit equality relating the determinants associated to a graph and to its dual graph. Also, they are proportional to the determinants of the discrete critical Laplacians on the graph G, exactly when the genus g is zero or one. Finally, they share several formal properties with the Ray-Singer \bar\partial-torsions of the Riemann surface in which G embeds.Comment: 30 pages, 10 figures; added section 4.4 in version

Fluctuations and skewness of the current in the partially asymmetric exclusion process

We use functional Bethe Ansatz equations to calculate the cumulants of the total current in the partially asymmetric exclusion process. We recover known formulas for the first two cumulants (mean value of the current and diffusion constant) and obtain an explicit finite size formula for the third cumulant. The expression for the third cumulant takes a simple integral form in the limit where the asymmetry scales as the inverse of the square root of the size of the system, which corresponds to a natural separation between weak and strong asymmetry.Comment: 21 pages, 3 figure

‘Still living with it even though it's gone’: Using interpretive phenomenological analysis to explore shared experiences of living with and beyond breast, prostate, and colorectal cancer

© 2021 The Authors. Purpose Living with and beyond cancer is an increasingly common experience. While research is uncovering valuable individual experiences of those living with and beyond cancer, it has been argued that this idiographic approach is limited in outlook, reach and impact. This study contributes to the understanding of what it means to live with and beyond cancer by complementing idiographic knowledge with multiple perspectives from a group of participants who are living with and beyond cancer, to explore how individual experiences may be relevant to others. Method Semi-structured interviews were conducted with people who had received treatment for breast (n = 6), prostate (n = 6) or colorectal cancer (n = 6). Data were analysed using interpretive phenomenological analysis. The early findings were then shared with a wider group of people who had received treatment for breast, prostate or colorectal cancer (n = 26) in six focus groups, to explore whether they had similar experiences. Results While individual accounts of living with and beyond cancer detail unique features specific to each person's experience, focus group discussions illustrated how participant life worlds interact and overlap. The findings identified thematic similarities within and between individual and group levels and across cancer types. Three super-ordinate themes describe the shared experience of living with and beyond cancer: i) the cancer shock, ii) managing cancer and getting through and iii) getting over cancer. Conclusions A multiple perspective approach informs our understanding of shared experiences of living with and beyond cancer. This knowledge can be used to direct, design, and deliver relevant supportive cancer care.Macmillan cancer support