Random Curves by Conformal Welding

We construct a conformally invariant random family of closed curves in the plane by welding of random homeomorphisms of the unit circle given in terms of the exponential of Gaussian Free Field. We conjecture that our curves are locally related to SLE$(\kappa)$ for $\kappa<4$.Comment: 5 page

Fourier's Law from Closure Equations

We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is proportional to the temperature gradient with a temperature dependent heat conductivity and the stationary temperature exhibits a nonlinear profile

Statistical Mechanics of Logarithmic REM: Duality, Freezing and Extreme Value Statistics of 1/f1/f Noises generated by Gaussian Free Fields

We compute the distribution of the partition functions for a class of one-dimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the two-dimensional Gaussian Free Field (2dGFF) along various planar curves. Our method extends the recent analysis of Fyodorov Bouchaud from the circular case to an interval and is based on an analytical continuation of the Selberg integral. In particular, we unveil a {\it duality relation} satisfied by the suitable generating function of free energy cumulants in the high-temperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2dGFF on the $[0,1]$ interval. We provide numerical checks of the circular and the interval case and discuss universality and various extensions. Relevance to the distribution of length of a segment in Liouville quantum gravity is noted.Comment: 25 pages, 12 figures Published version. Misprint corrected, references and note adde

Approach to ground state and time-independent photon bound for massless spin-boson models

It is widely believed that an atom interacting with the electromagnetic field (with total initial energy well-below the ionization threshold) relaxes to its ground state while its excess energy is emitted as radiation. Hence, for large times, the state of the atom+field system should consist of the atom in its ground state, and a few free photons that travel off to spatial infinity. Mathematically, this picture is captured by the notion of asymptotic completeness. Despite some recent progress on the spectral theory of such systems, a proof of relaxation to the ground state and asymptotic completeness was/is still missing, except in some special cases (massive photons, small perturbations of harmonic potentials). In this paper, we partially fill this gap by proving relaxation to an invariant state in the case where the atom is modelled by a finite-level system. If the coupling to the field is sufficiently infrared-regular so that the coupled system admits a ground state, then this invariant state necessarily corresponds to the ground state. Assuming slightly more infrared regularity, we show that the number of emitted photons remains bounded in time. We hope that these results bring a proof of asymptotic completeness within reach.Comment: 45 pages, published in Annales Henri Poincare. This archived version differs from the journal version because we corrected an inconsequential mistake in Section 3.5.1: to do this, a new paragraph was added after Lemma 3.

High Temperature Expansions and Dynamical Systems

We develop a resummed high-temperature expansion for lattice spin systems with long range interactions, in models where the free energy is not, in general, analytic. We establish uniqueness of the Gibbs state and exponential decay of the correlation functions. Then, we apply this expansion to the Perron-Frobenius operator of weakly coupled map lattices.Comment: 33 pages, Latex; [email protected]; [email protected]

Agile in the Era of Digitalization : A Finnish Survey Study

This paper was a Candidate for the Best Full Paper.Peer reviewe

Reviews and syntheses : Arctic fire regimes and emissions in the 21st century

In recent years, the pan-Arctic region has experienced increasingly extreme fire seasons. Fires in the northern high latitudes are driven by current and future climate change, lightning, fuel conditions, and human activity. In this context, conceptualizing and parameterizing current and future Arctic fire regimes will be important for fire and land management as well as understanding current and predicting future fire emissions. The objectives of this review were driven by policy questions identified by the Arctic Monitoring and Assessment Programme (AMAP) Working Group and posed to its Expert Group on Short-Lived Climate Forcers. This review synthesizes current understanding of the changing Arctic and boreal fire regimes, particularly as fire activity and its response to future climate change in the pan-Arctic have consequences for Arctic Council states aiming to mitigate and adapt to climate change in the north. The conclusions from our synthesis are the following. (1) Current and future Arctic fires, and the adjacent boreal region, are driven by natural (i.e. lightning) and human-caused ignition sources, including fires caused by timber and energy extraction, prescribed burning for landscape management, and tourism activities. Little is published in the scientific literature about cultural burning by Indigenous populations across the pan-Arctic, and questions remain on the source of ignitions above 70 degrees N in Arctic Russia. (2) Climate change is expected to make Arctic fires more likely by increasing the likelihood of extreme fire weather, increased lightning activity, and drier vegetative and ground fuel conditions. (3) To some extent, shifting agricultural land use and forest transitions from forest-steppe to steppe, tundra to taiga, and coniferous to deciduous in a warmer climate may increase and decrease open biomass burning, depending on land use in addition to climate-driven biome shifts. However, at the country and landscape scales, these relationships are not well established. (4) Current black carbon and PM2.5 emissions from wildfires above 50 and 65 degrees N are larger than emissions from the anthropogenic sectors of residential combustion, transportation, and flaring. Wildfire emissions have increased from 2010 to 2020, particularly above 60 degrees N, with 56% of black carbon emissions above 65 degrees N in 2020 attributed to open biomass burning - indicating how extreme the 2020 wildfire season was and how severe future Arctic wildfire seasons can potentially be. (5) What works in the boreal zones to prevent and fight wildfires may not work in the Arctic. Fire management will need to adapt to a changing climate, economic development, the Indigenous and local communities, and fragile northern ecosystems, including permafrost and peatlands. (6) Factors contributing to the uncertainty of predicting and quantifying future Arctic fire regimes include underestimation of Arctic fires by satellite systems, lack of agreement between Earth observations and official statistics, and still needed refinements of location, conditions, and previous fire return intervals on peat and permafrost landscapes. This review highlights that much research is needed in order to understand the local and regional impacts of the changing Arctic fire regime on emissions and the global climate, ecosystems, and pan-Arctic communities.peerReviewe