Random walks in Dirichlet environment: an overview

Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on $\Bbb{Z}^d$ where the transition probabilities are i.i.d. at each site with a Dirichlet distribution. Hence, the model is parametrized by a family of positive weights $(\alpha_i)_{i=1, \ldots, 2d}$, one for each direction of $\Bbb{Z}^d$. In this case, the annealed law is that of a reinforced random walk, with linear reinforcement on directed edges. RWDE have a remarkable property of statistical invariance by time reversal from which can be inferred several properties that are still inaccessible for general environments, such as the equivalence of static and dynamic points of view and a description of the directionally transient and ballistic regimes. In this paper we give a state of the art on this model and several sketches of proofs presenting the core of the arguments. We also present new computation of the large deviation rate function for one dimensional RWDE.Comment: 35 page

Does Collateral Help Mitigate Adverse Selection ? A Cross-Country Analysis

We investigate whether collateral helps to solve adverse selection problems. Theory predicts a negative relationship between presence of collateral and risk premium, as collateral constitutes a signalling instrument for the borrower to be charged with a lower risk premium. However, bankers’ view and most empirical evidence contradict this prediction in accordance with the observed-risk hypothesis. We provide new evidence with loan-level data and country-level data for a sample of 5843 bank loans from 43 countries. We test whether the degree information asymmetries affects the link between the presence of collateral and risk premium. We include five proxies for the degree of information asymmetries, measuring opacity of financial information, trust, and development. We find that a greater degree of information asymmetries reduces the positive relationship between the presence of collateral and the risk premium. This finding provides support for the adverse selection and observed-risk hypotheses, as both hypotheses may be empirically validated depending of the degree of information asymmetries in the country.Collateral; Bank; Asymmetric information; Institutions

Microcontact printing process for the patterned growth of individual CNTs

We report an original approach to pattern a substrate with isolated carbon nanotubes. Through the improvement of the microcontact printing technique by the use of a new composite stamp, we were able to produce on flat substrates micrometric features of a catalyst suitable for the localised growth of single-walled carbon nanotubes by catalytic chemical vapour deposition. This catalyst material is for the first time prepared via an original sol–gel process. The growth of straight carbon nanotubes between the patterns was observed and a method to promote the controlled growth of such isolated nanoobjects is thus conceivable

M\"obius inversion formula for monoids with zero

The M\"obius inversion formula, introduced during the 19th century in number theory, was generalized to a wide class of monoids called locally finite such as the free partially commutative, plactic and hypoplactic monoids for instance. In this contribution are developed and used some topological and algebraic notions for monoids with zero, similar to ordinary objects such as the (total) algebra of a monoid, the augmentation ideal or the star operation on proper series. The main concern is to extend the study of the M\"obius function to some monoids with zero, i.e., with an absorbing element, in particular the so-called Rees quotients of locally finite monoids. Some relations between the M\"obius functions of a monoid and its Rees quotient are also provided.Comment: 12 pages, r\'esum\'e \'etendu soumis \`a FPSAC 201

The weight and density of carbon nanotubes versus the number of walls and diameter

The weight and density of carbon nanotubes are calculated as a function of their characteristics (inner diameter, outer diameter, and number of walls). The results are reported in the form of diagrams which may be useful to other researchers, in particular in the fields of synthesis/production, materials and composites, health/toxicity studies

Curvature singularity and film-skating during drop impact

We study the influence of the surrounding gas in the dynamics of drop impact on a smooth surface. We use an axisymmetric 3D model for which both the gas and the liquid are incompressible; lubrication regime applies for the gas film dynamics and the liquid viscosity is neglected. In the absence of surface tension a finite time singularity whose properties are analysed is formed and the liquid touches the solid on a circle. When surface tension is taken into account, a thin jet emerges from the zone of impact, skating above a thin gas layer. The thickness of the air film underneath this jet is always smaller than the mean free path in the gas suggesting that the liquid film eventually wets the surface. We finally suggest an aerodynamical instability mechanism for the splash.Comment: 5 figure

Partial monoids: associativity and confluence

A partial monoid $P$ is a set with a partial multiplication $\times$ (and total identity $1_P$) which satisfies some associativity axiom. The partial monoid $P$ may be embedded in a free monoid $P^*$ and the product $\star$ is simulated by a string rewriting system on $P^*$ that consists in evaluating the concatenation of two letters as a product in $P$, when it is defined, and a letter $1_P$ as the empty word $\epsilon$. In this paper we study the profound relations between confluence for such a system and associativity of the multiplication. Moreover we develop a reduction strategy to ensure confluence and which allows us to define a multiplication on normal forms associative up to a given congruence of $P^*$. Finally we show that this operation is associative if, and only if, the rewriting system under consideration is confluent

Catalytic CVD Synthesis of Double and Triple-walled Carbon Nanotubes by the Control of the Catalyst Preparation

We report the influence of catalyst preparation conditions for the synthesis of carbon nanotubes (CNTs) by catalytic chemical vapour deposition (CCVD). Catalysts were prepared by the combustion route using either urea or citric acid as the fuel. We found that the milder combustion conditions obtained in the case of citric acid can either limit the formation of carbon nanofibres (defined as carbon structures not composed of perfectly co-axial walls or only partially tubular) or increase the selectivity of the CCVD synthesis towards CNTs with fewer walls, depending on the catalyst composition. It is thus for example possible in the same CCVD conditions to prepare (with a catalyst of identical chemical composition) either a sample containing more than 90% double- and triple-walled CNTs, or a sample containing almost 80% double-walled CNTs

Collateral and Adverse Selection in Transition Countries

This paper tackles the question of knowing whether collateral helps solve adverse selection problems in transition countries. We use a unique dataset of about 400 bank loans from 16 transition countries. Our findings support the view of a positive link between the presence of collateral and the risk premium, which is in accordance with the observed-risk hypothesis. This suggests that collateral does not mitigate adverse selection problems in transition countries.Bank, collateral, transition economies.