Finite temperature Functional RG, droplets and decaying Burgers Turbulence

The functional RG (FRG) approach to pinning of $d$-dimensional manifolds is reexamined at any temperature $T$. A simple relation between the coupling function $R(u)$ and a physical observable is shown in any $d$. In $d=0$ its beta function is displayed to a high order, ambiguities resolved; for random field disorder (Sinai model) we obtain exactly the T=0 fixed point $R(u)$ as well as its thermal boundary layer (TBL) form (i.e. for $u \sim T$) at $T>0$. Connection between FRG in $d=0$ and decaying Burgers is discussed. An exact solution to the functional RG hierarchy in the TBL is obtained for any $d$ and related to droplet probabilities.Comment: 8 pages 1 figur

Strain and the inflation - unemployment relationship: a conceptual and empirical investigation

Economic theory tells that a command system allocates resources poorly because of the impossibility of economic calculation. Therefore, once prices are freed and start to operate at quasi-equilibrium (market-clearing) levels, the hidden inefficiencies come into the open and a massive resource reallocation would have to take place. More precisely, the issue refers to the possible and probable intensity of resource reallocation in view of constraints like the balance between exit and entry in the labour market, the size of the budget deficit and the means for its non-inflationary financing, social and political stability, etc. This paper makes an attempt to conceptualise the emergence of strain emerges an economic system when relative prices change dramatically, and explores what can be implications for stabilisation policy. The start is made with the closed economy, after which the open economy case is looked at, and a possible formalised expression of strain is suggested, The distributional struggle, as a consequence of resource reallocation, is highlighted. Some modelling and empirical analysis help in substantiating the main thesis. it is contented that the line of reasoning espoused herein can help in developing an economic explanation of shocks in economic systems.open economy; Phillips curve; long-run atractor; fractal dimension

Author's response: Mundari and argumentation in word-class analysis

1. Introduction: Our three commentators raise such a host of deep and interesting issues that we cannot hope to answer them all within the time and space at our disposal. To begin with, we would like to thank them for pushing us to articulate the reason

A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting nonlinear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes.Comment: v2 (55 pages): many improvements on the presentation, v3: correction of a few typos, to appear In Probability Theory and Related Field