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We give an invariance principle for very general additive functionals of conditioned Bienaymé-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Lévy tree. This includes the case when the offspring distribution has finite variance (the Lévy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending on the size and height. [ABSTRACT FROM AUTHOR]

We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove that, up to a deterministic time-change, it is distributed as a continuous-time Galton–Watson process with immigration. We obtain similar results for a critical stable branching mechanism when only looking at immigrants arriving in some fixed time-interval. For a general sub-critical branching mechanism, we consider the number of individuals that give descendants in the extant population. The associated processes (forward or backward in time) are pure-death or pure-birth Markov processes, for which we compute the transition rates. [ABSTRACT FROM AUTHOR]

We apply the penalization technique introduced by Roynette, Vallois, Yor for Brownian motion to Galton–Watson processes with a penalizing function of the form P (x) s x where P is a polynomial of degree p and s ∈ [ 0 , 1 ]. We prove that the limiting martingales obtained by this method are most of the time classical ones, except in the super-critical case for s = 1 (or s → 1) where we obtain new martingales. If we make a change of probability measure with this martingale, we obtain a multi-type Galton–Watson tree with p distinguished infinite spines. [ABSTRACT FROM AUTHOR]

Battiau-Queney, Y.; Ventalon, S.; Abraham, R.; Sipka, V.; Cohen, O., and Marin, D., 2024. Bedforms and sedimentary features related to water-depth variations in a sandy tidal-flat environment. Journal of Coastal Research, 40(1), 80–103. Charlotte (North Carolina), ISSN 0749-0208. This study highlighted the variability of a wide sandy macrotidal coastal system on short timescales. Changes in water depth and exposure length were the main drivers of this variability. In the study area, the coastal system consists of three units: a lower ridge-and-runnel beach, a 1000-m-wide tidal flat, and a sandy backshore. This research is based on sedimentary features that can record physical forces, especially the bedforms at the beach surface, and their relationship with beach gradient, exposure length, and changing water depth, according to tidal, weather, and marine conditions. It also demonstrated the ability of scanning electron microscope analysis of quartz grain microtextures to indicate the level of marine and eolian energy in the coastal system. The widespread wave and current sand ripples on the tidal flat showed great variability in time and space. A minimum water depth of 0.30 to 0.50 m was required for their development. The role of wind-induced waves and the frequent interference of tidal, wave, and wind forcing mechanisms are emphasized. The development of some complex sand ripples extended over a complete lunar tidal cycle. Wind-generated sand ripples were observed only on the backshore. Their absence on the tidal flat, despite the high level of eolian energy attested by quartz microtextures, and the poor development of dunes on the backshore are explained by factors impeding eolian sand transport at the beach surface such as extreme fetch segmentation and possible shell armoring of the beach surface during dry periods. This study demonstrated the short-term variability of the beach morphology as opposed to the long-term stability of the coastal system as a whole, in which the ultradissipative tidal flat, characterized by limited sand supply, low wave energy, and high but inefficient wind energy, plays a key role. [ABSTRACT FROM AUTHOR]

We consider the Brownian tree introduced by Aldous and the associated Q-process which consists in an infinite spine on which are grafted independent Brownian trees. We present a reversal procedure on these trees that consists in looking at the tree downward from its top: the branching points becoming leaves and leaves becoming branching points. We prove that the distribution of this tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas (2016). [ABSTRACT FROM AUTHOR]

We study the pruning process developed by Abraham and Delmas (2012) on the discrete Galton–Watson sub-trees of the Lévy tree which are obtained by considering the minimal sub-tree connecting the root and leaves chosen uniformly at rate λ , see Duquesne and Le Gall (2002). The tree-valued process, as λ increases, has been studied by Duquesne and Winkel (2007). Notice that we have a tree-valued process indexed by two parameters: the pruning parameter θ and the intensity λ . Our main results are: construction and marginals of the pruning process, representation of the pruning process (forward in time that is as θ increases) and description of the growing process (backward in time that is as θ decreases) and distribution of the ascension time (or explosion time of the backward process) as well as the tree at the ascension time. A by-product of our result is that the super-critical Lévy trees independently introduced by Abraham and Delmas (2012) and Duquesne and Winkel (2007) coincide. This work is also related to the pruning of discrete Galton–Watson trees studied by Abraham, Delmas and He (2012). [ABSTRACT FROM AUTHOR]

Representation of coalescent processes using pruning of trees has been used by Goldschmidt and Martin for the Bolthausen-Sznitman coalescent and by Abraham and Delmas for the β(3/2, 1/2)-coalescent. By considering a pruning procedure on stable Galton-Watson tree with n labeled leaves, we give a representation of the discrete β(1+α, 1-α)-coalescent, with α ∈ [1/2, 1) starting from the trivial partition of the n first integers. The construction can also be made directly on the stable continuum Lévy tree, with parameter 1/α, simultaneously for all n. This representation allows to use results on the asymptotic number of coalescence events to get the asymptotic number of cuts in stable Galton-Watson tree (with infinite variance for the offspring distribution) needed to isolate the root. Using convergence of the stable Galton-Watson tree conditioned to have infinitely many leaves, one can get the asymptotic distribution of blocks in the last coalescence event in the β(1 + α, 1 - α)-coalescent. [ABSTRACT FROM AUTHOR]

We give an explicit construction of the increasing tree-valued process introduced by Abraham and Delmas using a random point process of trees and a grafting procedure. This random point process will be used in companion papers to study record processes on Lévy trees. We use the Poissonian structure of the jumps of the increasing tree-valued process to describe its behavior at the first time the tree grows higher than a given height, using a spinal decomposition of the tree, similar to the classical Bismut and Williams decompositions. We also give the joint distribution of this exit time and the ascension time which corresponds to the first infinite jump of the tree-valued process. [ABSTRACT FROM AUTHOR]

We perform a pruning procedure on a Lévy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the Lévy tree). We prove that the tree constructed by regrafting is distributed as the original Lévy tree, generalizing a result of Addario-Berry, Broutin and Holmgren where only Aldous’s tree is considered. As a consequence, we obtain that the “average pruning time” of a leaf is distributed as the height of a leaf picked at random in the Lévy tree. [ABSTRACT FROM AUTHOR]

Abstract: We consider an initial Eve-population and a population of neutral mutants, such that the total population dies out in finite time. We describe the evolution of the Eve-population and the total population with continuous state branching processes, and the neutral mutation procedure can be seen as an immigration process with intensity proportional to the size of the population. First we establish a Williams’ decomposition of the genealogy of the total population given by a continuum random tree, according to the ancestral lineage of the last individual alive. This allows us to give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population. [Copyright &y& Elsevier]

We consider an initial population whose size evolves according to a continuous state branching process. Then we add to this process an immigration (with the same branching mechanism as the initial population), in such a way that the immigration rate is proportional to the whole population size. We prove this continuous state branching process with immigration proportional to its own size is itself a continuous state branching process. By considering the immigration as the apparition of a new type, this construction is a natural way to model neutral mutation. It also provides in some sense a dual construction of the particular pruning at nodes of continuous state branching process introduced by the authors in a previous paper. For a critical or sub-critical quadratic branching mechanism, it is possible to explicitly compute some quantities of interest. For example, we compute the Laplace transform of the size of the initial population conditionally on the non-extinction of the whole population with immigration. We also derive the probability of simultaneous extinction of the initial population and the whole population with immigration. [ABSTRACT FROM AUTHOR]

We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using Lévy snake tools developed by Le Gall-Le Jan and Duquesne-Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. We also give a special Markov property for the snake which is of its own interest. [ABSTRACT FROM AUTHOR]

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We consider the exit measure of super Brownian motion with a stable branching mechanism of a smooth domain D of ℝ[sup d] . We derive lower bounds for the hitting probability of small balls for the exit measure and upper bounds in the critical dimension. This completes results given by Sheu [22] and generalizes the results of Abraham and Le Gall [2]. Because of the links between exits measure and partial differential equations, those results imply bounds on solutions of elliptic semi-linear PDE. We also give the Hausdorff dimension of the support of the exit measure and show it is totally disconnected in high dimension. Eventually we prove the exit measure is singular with respect to the surface measure on ∂D in the critical dimension. Our main tool is the subordinated Brownian snake introduced by Bertoin, Le Gall and Le Jan [4]. [ABSTRACT FROM AUTHOR]

Black shales, though laminated, are not systematically synonymous with quiet conditions of deposition. A number of papers report about black shales yielding sedimentary structures echoing relatively high hydrodynamic conditions. Here we examine two sedimentary sequences pertaining to the Late Jurassic Argiles de Châtillon Formation of the Boulonnais area (Northernmost France), each of them including a meter-thick black-shale horizon. The two laminated black shales contain sulfurized (i.e., organic S-rich) organic matter, reaching a maximum of 9%. However, some differences set the two black shales apart. The lower one was deposited under calm, suboxic to anoxic, bottom-water conditions (the « classic » way); the upper black shale was deposited under oxic, agitated bottom-water conditions, not compatible with stable sulfidic conditions required for organic-matter sulfurization. The upper black shale experienced hydrodynamically-induced concentration of sulfurized, recalcitrant organic matter of marine origin. The sulfurized organic matter could be preserved and quantitatively accumulated owing to its non-putrescible nature, leading to the formation of a potential hydrocarbon source rock. The association of pyrite inclusions with sulfurized organic matter probably modified the hydrodynamic behavior of organic particles. The storm-induced remobilization and concentration of sulfurized organic matter implies that the "sulfurization factory" operated in proximal, shallow environments such as estuaries, mud flats or mangrove environments. Such a model is in agreement with findings from modern coastal/shelf environments (notably mangroves) and fully transposable to many other sedimentary situations of any geological time period. • Some specific black shales were deposited under agitated conditions. • They contain sulfurized organic matter of marine origin. • They are associated with tempestites. • Sulfurized OM was remobilized from proximal setting. [ABSTRACT FROM AUTHOR]

At Cap Blanc Nez (Channel coast, France), the chalk of the Lower Cenomanian is very rich in glauconite. Glauconite is of authigenic origin and requires the mobilization of chemical elements for its growth: Si, Fe and K. If we already know thanks to elementary geochemistry (Ge/Si ratio) that the silica of the flint present in the chalk originates from the dissolution of sponges, is it the same for glauconite? This question only makes sense if glauconite is proved to be autochthonous and synsedimentary, and not reworked during the Cenomanian transgression. In addition, we wanted to know whether the study of the content of trace elements in glauconite could provide information on the conditions of authigenesis in glauconious chalk. The clay content of the chalk from the Lower Cenomanian has been examined and the green minerals were extracted from the rock to study their morphology, mineralogy, geochemistry (major & trace elements) and grain size. The chalk consists of calcium carbonate, smectite and true glauconite, in the form of pellets, sometimes with rare traces of quartz and some centimeter-scale phosphate gravel. The grain-size distribution of the glauconites varies from one sample to another and is always poorly sorted, which militates in favor of an autochthonous (not reworked) origin of these minerals. This origin is also suggested by the virtual absence of terrigenous minerals, except for smectite known for its potential for wide distribution in the marine environment. The geochemistry of the samples shows a very homogeneous composition of major and trace elements, with a K 2 O content greater than 8%. This characterizes these glauconites as being very evolved, which indicates a long authigenic formation time (> 100 ky) and therefore an extremely reduced or irregular sedimentation rate. Here, glauconites are very rich in germanium, which makes it impossible to identify a source of silica (unlike what is possible with flints). It cannot therefore be said that the silica results from the dissolution of sponges but this enrichment in Ge, coupled with that in vanadium and the absence of enrichment in molybdenum, indicates a slightly reducing deposition milieu (suboxic). Such conditions usually favor organic matter accumulation, but not here, due to protracted sedimentation hiatuses. Lastly, glauconite trapped relatively large amounts of Ge due to reducing conditions and long exposure time to seawater, which makes it a potential chronometer assessing the duration of authigenesis, and a possible compartment of the marine cycle of germanium. [ABSTRACT FROM AUTHOR]