Large deviations of branching process in a random environment

In this first part of the paper we find the asymptotic formulas for the probabilities of large deviations of the sequence defined by the random difference equation Y n+1=A n Y n + B n , where A 1, A 2, … are independent identically distributed random variables and B n may depend on { ( A k , B k ) , 0 ⩽ k < n } $ \{(A_k,B_k),0\leqslant k \lt n\} $ for any n≥1. In the second part of the paper this results are applied to the large deviations of branching processes in a random environment.

On uniqueness of invariant measures for random walks on

We consider random walks on the group of orientation-preserving homeomorphisms of the real line ${\mathbb R}$ . In particular, the fundamental question of uniqueness of an invariant measure of the generated process is raised. This problem was studied by Choquet and Deny [Sur l’équation de convolution $\mu = \mu * \sigma $ . C. R. Acad. Sci. Paris250 (1960), 799–801] in the context of random walks generated by translations of the line. Nowadays the answer is quite well understood in general settings of strongly contractive systems. Here we focus on a broader class of systems satisfying the conditions of recurrence, contraction and unbounded action. We prove that under these conditions the random process possesses a unique invariant Radon measure on ${\mathbb R}$ . Our work can be viewed as following on from Babillot et al [The random difference equation $X_n=A_n X_{n-1}+B_n$ in the critical case. Ann. Probab.25(1) (1997), 478–493] and Deroin et al [Symmetric random walk on $\mathrm {HOMEO}^{+}(\mathbb {R})$ . Ann. Probab.41(3B) (2013), 2066–2089].

ENVIRONMENTAL STRESS AND FLUCTUATING ASYMMETRY IN ANTILOPHIA GALEATA, MYIOTHLYPIS FLAVEOLA AND BASILEUTERUS CULICIVORUS IN BRAZILIAN SAVANNA

Fluctuating asymmetry (FA), defined as the random difference between two sides of a bilaterally symmetrical character, is often used to monitor biological populations in altered habitats. We aimed to compare the values of FA for wing and tarsi of three bird species (Antilophia galeata, Myiothlypis flaveola and Basileuterus culicivorus) in areas with different environmental stresses and to analyze their potential use as biomonitors. The birds were captured between March 2010 and March 2011, in seven forest fragments. In areas of high environmental stress, FA was higher for the wings of A. galeata and M. flaveola and the tarsi of B. culicivorus. FA depends on the functional importance of the character for each species. Thus, this study demonstrated that FA in wings and tarsi is a useful tool to assess the quality of the Brazilian Savanna (Cerrado) forest habitat.

Validation of Aeolus Rayleigh and Mie winds using atmospheric radars in Arctic Sweden and in Antarctica

&lt;p&gt;So far, validation of Aeolus winds for the polar regions has been based on the ECMWF global data assimilation and forecasting system (e.g. Rennie and Isaksen 2020). &amp;#160;Very few conventional upper air meteorological measurements (radiosondes, aircraft in-situ sensors) are available in the polar regions so the model&amp;#8217;s accuracy is not well known in those regions. &amp;#160;There is a risk that different cloud conditions, surface reflectivities and summer daylight in these regions could lead to different performance of the space-borne lidar measurements. At the same time, accurate measurements over the polar regions would be a particular asset to global weather forecasting and climate monitoring as these regions are so poorly covered by other observations. We validate Aeolus Rayleigh and Mie winds by comparison with winds measured by two atmospheric radars, ESRAD and MARA, located at Esrange (68&amp;#176;N 21&amp;#176;E) in Arctic Sweden and at the Indian Antarctic station Maitri (71&amp;#176;S 12&amp;#176;E), respectively, for the period July - December 2019 when reprocessed data for baseline 10 with the telescope mirror temperature correction were available. Data were divided into two seasons: summer with 12 -24 hours direct sunlight and winter covering the rest of the time. Aeolus - radar collocation events are defined when the distance between Aeolus measurement swath and the radar sites is less than 100 km. We computed regression, bias, and standard deviation for the Aeolus winds in comparison with the radars. For Rayleigh winds the slope of regression line is not significantly different from 1, and bias is not significantly different from 0.&amp;#160; Random difference (std) is 4.4 m/s &amp;#8211; 7 m/s. For Rayleigh winds at both locations and Mie winds at Esrange we did not find any statistically significant difference between ascending/descending orbits and seasons. However, at Maitri, Antarctica a few m/s bias is found for Mie winds in summer for ascending (evening) passes.&lt;/p&gt;

Null recurrence and transience of random difference equations in the contractive case

Given a sequence (Mk, Qk)k ≥ 1 of independent and identically distributed random vectors with nonnegative components, we consider the recursive Markov chain (Xn)n ≥ 0, defined by the random difference equation Xn = MnXn - 1 + Qn for n ≥ 1, where X0 is independent of (Mk, Qk)k ≥ 1. Criteria for the null recurrence/transience are provided in the situation where (Xn)n ≥ 0 is contractive in the sense that M1 ⋯ Mn → 0 almost surely, yet occasional large values of the Qn overcompensate the contractive behavior so that positive recurrence fails to hold. We also investigate the attractor set of (Xn)n ≥ 0 under the sole assumption that this chain is locally contractive and recurrent.

Validated Simulations of Heat Transfer From a Vertical Heated-Rod Array to a Helium-Filled Isothermal Enclosure

Measurements of heat transfer from an array of vertical heater rods to the walls of a square, helium-filled enclosure are performed for a range of enclosure temperatures, helium pressures, and rod heat generation rates. This configuration is relevant to a used nuclear fuel assembly within a dry storage canister. The measurements are used to assess the accuracy of computational fluid dynamics (CFD)/radiation simulations in the same configuration. The simulations employ the measured enclosure temperatures as boundary conditions and predict the temperature difference between the rods and enclosure. These temperature differences are as large as 72 °C for some experiments. The measured temperature of rods near the periphery of the array is sensitive to small, uncontrolled variations in their location. As a result, those temperatures are not as useful for validating the simulations as measurements from rods near the array center. The simulated rod temperatures exhibit random differences from the measurements that are as large as 5.7 °C, but the systematic (average) error is 1 °C or less. The random difference between the simulated and measured maximum array temperature is 2.1 °C, which is less than 3% of the maximum rod-to-wall temperature difference.