arXiv subjects

R. J. Williams

Publications and source records attributed to R. J. Williams.

13 recordsLinked to original sources

arXiv2021

Limit theorems and ergodicity for general bootstrap random walks

Given the increments of a simple symmetric random walk $(X_n)_{n\ge0}$, we characterize all possible ways of recycling these increments into a simple symmetric random walk $(Y_n)_{n\ge0}$ adapted to the filtration of $(X_n)_{n\ge0}$. We study the long term behavior of a suitably normalized two-dimensional process $((X_n,Y_n))_{n\ge0}$. In particular, we provide necessary and sufficient conditions for the process to converge to a two-dimensional Brownian motion (possibly degenerate). We also discuss cases in which the limit is not Gaussian. Finally, we provide a simple necessary and sufficient condition for the ergodicity of the recycling transformation, thus generalizing results from Dubins and Smorodinsky (1992) and Fujita (2008), and solving the discrete version of the open problem of the ergodicity of the general Lévy transformation (see Mansuy and Yor, 2006).

math.PR↗

arXiv2017

An ultra-dense fast outflow in a quasar at z=2.4

We present Adaptive Optics assisted near-IR integral field spectroscopic observations of a luminous quasar at $z = 2.4$, previously observed as the first known example at high redshift of large scale quasar-driven outflow quenching star formation in its host galaxy. The nuclear spectrum shows broad and blueshifted H$β$ in absorption, which is tracing outflowing gas with high densities ($>10^8$ - $10^9$ cm$^{-3}$) and velocities in excess of 10,000 km s$^{-1}$. The properties of the outflowing clouds (covering factor, density, column density and inferred location) indicate that they likely originate from the Broad Line Region. The energetics of such nuclear regions are consistent with that observed in the large scale outflow, supporting models in which quasar driven outflows originate from the nuclear region and are energy conserving. We note that the asymmetric profile of both the H$β$ and H$α$ emission lines is likely due to absorption by the dense outflowing gas along the line of sight. This outflow-induced asymmetry has implications on the estimation of the black hole mass using virial estimators, and warns about such effects for several other quasars characterized by similar line asymmetries. More generally, our findings may suggest a broader revision of the decomposition and interpretation of quasar spectral features, in order to take into account the presence of potential broad blueshifted Balmer absorption lines. Our high spatial resolution data also reveals redshifted, dynamically colder nebular emission lines, likely tracing an inflowing stream.

astro-ph.GA↗

arXiv2015

ALMA constraints on the faint millimetre source number counts and their contribution to the cosmic infrared background

We have analysed 18 ALMA continuum maps in Bands 6 and 7, with rms down to 7.8$μ$Jy, to derive differential number counts down to 60$μ$Jy and 100$μ$Jy at $λ=$1.3 mm and $λ=$1.1 mm, respectively. The area covered by the combined fields is $\rm 9.5\times10^{-4}deg^2$ at 1.1mm and $\rm 6.6\times10^{-4}deg^{2}$ at 1.3mm. We improved the source extraction method by requiring that the dimension of the detected sources be consistent with the beam size. This method enabled us to remove spurious detections that have plagued the purity of the catalogues in previous studies. We detected 50 faint sources with S/N$>$3.5 down to 60$μ$Jy, hence improving the statistics by a factor of four relative to previous studies. The inferred differential number counts are $\rm dN/d(Log_{10}S)=1\times10^5~deg^2$ at a 1.1 mm flux $S_{λ= 1.1~mm} = 130~μ$Jy, and $\rm dN/d(Log_{10}S)=1.1\times10^5~deg^2$ at a 1.3 mm flux $\rm S_{λ= 1.3~mm} = 60~μ$Jy. At the faintest flux limits, i.e. 30$μ$Jy and 40$μ$Jy, we obtain upper limits on the differential number counts of $\rm dN/d(Log_{10}S) < 7\times10^5~deg^2$ and $\rm dN/d(Log_{10}S)<3\times10^5~deg^2$, respectively. Our results provide a new lower limit to CIB intensity of 17.2${\rm Jy\ deg^{-2}}$ at 1.1mm and of 12.9${\rm Jy\ deg^{-2}}$ at 1.3mm. Moreover, the flattening of the integrated number counts at faint fluxes strongly suggests that we are probably close to the CIB intensity. Our data imply that galaxies with SFR$<40~M_{\odot}/yr$ certainly contribute less than 50% to the CIB while more than 50% of the CIB must be produced by galaxies with $\rm SFR>40~M_{\odot}/yr$. The differential number counts are in nice agreement with recent semi-analytical models of galaxy formation even as low as our faint fluxes. Consequently, this supports the galaxy evolutionary scenarios and assumptions made in these models.

astro-ph.GA↗

arXiv2014

Dynamics and Metallicity of Far-IR Selected Galaxies

We present near-infrared integral field spectroscopy of ten Herschel selected galaxies at z~1.5. From detailed mapping of the H$α$ and [NII] emission lines we trace the dynamics, star formation rates, metallicities and also investigate gas fractions for these galaxies. For a few galaxies the distribution of star formation as traced by H$α$ only traces a small fraction of the stellar disc, which could be tracing recent minor merging events. The rest-frame ultraviolet (UV) continuum emission often has a distribution completely different from H$α$, which warns about the use of UV-SED based star formation tracers in these systems. Our analysis of galaxy dynamics shows that minor dynamical disruptions (e.g. minor merging) are generally not enough to cause a deviation from the established 'Main Sequence' relation. Most galaxies are found to follow the fundamental metallicity relation (FMR), although with large scatter. One galaxy, (a small satellite galaxy of a massive companion) is found to deviate strongly from the FMR. This deviation is in nice agreement with the correlation recently discovered in local galaxies between gas metallicity and environment, which has been ascribed to enriched inter-galactic medium (IGM) in dense environments, and therefore suggests that here the IGM was already significantly enriched by z~1.5.

astro-ph.GA↗

arXiv2014

Constraining the Nature of Two Ly-alpha Emitters detected by ALMA at z = 4.7

We report optical VLT FORS2 spectroscopy of the two Ly-alpha emitters (LAEs) companions to the quasi-stellar object (QSO) - sub-millimetre galaxy (SMG) system BRI1202-0725 at z = 4.7, which have recently been detected in the [CII]158um line by the Atacama Large Millimetre/Sub-millimetre Array (ALMA). We detect Ly-alpha emission from both sources and so confirm that these Ly-alpha emitter candidates are physically associated with the BRI1202- 0725 system. We also report the lack of detection of any high ionisation emission lines (N V, Si IV, C IV and He II) and find that these systems are likely not photoionised by the quasar, leaving in situ star formation as the main powering source of these LAEs. We also find that both LAEs have Ly-alpha emission much broader (1300 km/s) than the [CII] emission and broader than most LAEs. In addition, both LAEs have roughly symmetric Ly-alpha profiles implying that both systems are within the HII sphere produced by the quasar. This is the first time that the proximity zone of a quasar is probed by exploiting nearby Ly-alpha emitters. We discuss the observational properties of these galaxies in the context of recent galaxy formation models.

astro-ph.GA↗

arXiv2013

HerMES: The Contribution to the Cosmic Infrared Background from Galaxies Selected by Mass and Redshift

We quantify the fraction of the cosmic infrared background (CIB) that originates from galaxies identified in the UV/optical/near-infrared by stacking 81,250 (~35.7 arcmin^2) K-selected sources (K_AB < 24.0), split according to their rest-frame U - V vs. V - J colors into 72,216 star-forming and 9,034 quiescent galaxies, on maps from Spitzer/MIPS (24um), Herschel/SPIRE (250, 350, 500um), Herschel/PACS (100, 160um), and AzTEC (1100um). The fraction of the CIB resolved by our catalog is (69 $\pm$ 15)% at 24um, (78 $\pm$ 17)% at 70um, (58 $\pm$ 13)% at 100um, (78 $\pm$ 18)% at 160um, (80 $\pm$ 17)% at 250um, (69 $\pm$ 14)% at 350um, (65 $\pm$ 12)% at 500um, and (45 $\pm$ 8)% at 1100um. Of that total, about 95% originates from star-forming galaxies, while the remaining 5% is from apparently quiescent galaxies. The CIB at $λ$ < 200um is sourced predominantly from galaxies at z < 1, while at $λ$ > 200um the bulk originates from 1 < z < 2. Galaxies with stellar masses log(M/ M_sun)=9.5-11 are responsible for the majority of the CIB, with those in the log(M/ M_sun)=9.5-10 contributing mostly at $λ$ < 250um, and those in the log(M/ M_sun)=10.5-11 bin dominating at $λ$ > 350um. The contribution from galaxies in the log(M/ M_sun)=9.0-9.5 and log(M/ M_sun)=11.0-12.0 stellar mass bins contribute the least, both of order 5%, although the highest stellar-mass bin is a significant contributor to the luminosity density at z > 2. The luminosities of the galaxies responsible for the CIB shifts from a combination of "normal" and luminous infrared galaxies (LIRGs) at $λ$ < 160um, to LIRGs at 160um < $λ$ < 500um, to finally LIRGs and ultra-luminous infrared galaxies (ULIRGs) at $λ$ > 500um. Stacking analyses were performed with SIMSTACK (available at http://www.astro.caltech.edu/~viero/viero_homepage/toolbox.html) which accounts for possible biases due to clustering.

astro-ph.CO↗

arXiv2012

State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy

We consider a connection-level model of Internet congestion control, introduced by Massoulié and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. Here, bandwidth is shared fairly among elastic document transfers according to a weighted $α$-fair bandwidth sharing policy introduced by Mo and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567] [$α\in (0,\infty)$]. Assuming Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. A fluid model (or functional law of large numbers approximation) for this stochastic model was derived and analyzed in a prior work [Ann. Appl. Probab. 14 (2004) 1055--1083] by two of the authors. Here, we use the long-time behavior of the solutions of the fluid model established in that paper to derive a property called multiplicative state space collapse, which, loosely speaking, shows that in diffusion scale, the flow count process for the stochastic model can be approximately recovered as a continuous lifting of the workload process.

math.PR↗

arXiv2010

Heavy traffic on a controlled motorway

Unlimited access to a motorway network can, in overloaded conditions, cause a loss of capacity. Ramp metering (signals on slip roads to control access to the motorway) can help avoid this loss of capacity. The design of ramp metering strategies has several features in common with the design of access control mechanisms in communication networks. Inspired by models and rate control mechanisms developed for Internet congestion control, we propose a Brownian network model as an approximate model for a controlled motorway and consider it operating under a proportionally fair ramp metering policy.We present an analysis of the performance of this model.

math.PR↗

arXiv2007

An invariance principle for semimartingale reflecting Brownian motions in domains with piecewise smooth boundaries

Semimartingale reflecting Brownian motions (SRBMs) living in the closures of domains with piecewise smooth boundaries are of interest in applied probability because of their role as heavy traffic approximations for some stochastic networks. In this paper, assuming certain conditions on the domains and directions of reflection, a perturbation result, or invariance principle, for SRBMs is proved. This provides sufficient conditions for a process that satisfies the definition of an SRBM, except for small random perturbations in the defining conditions, to be close in distribution to an SRBM. A crucial ingredient in the proof of this result is an oscillation inequality for solutions of a perturbed Skorokhod problem. We use the invariance principle to show weak existence of SRBMs under mild conditions. We also use the invariance principle, in conjunction with known uniqueness results for SRBMs, to give some sufficient conditions for validating approximations involving (i) SRBMs in convex polyhedrons with a constant reflection vector field on each face of the polyhedron, and (ii) SRBMs in bounded domains with piecewise smooth boundaries and possibly nonconstant reflection vector fields on the boundary surfaces.

math.PR↗

arXiv2006

Workload reduction of a generalized Brownian network

We consider a dynamic control problem associated with a generalized Brownian network, the objective being to minimize expected discounted cost over an infinite planning horizon. In this Brownian control problem (BCP), both the system manager's control and the associated cumulative cost process may be locally of unbounded variation. Due to this aspect of the cost process, both the precise statement of the problem and its analysis involve delicate technical issues. We show that the BCP is equivalent, in a certain sense, to a reduced Brownian control problem (RBCP) of lower dimension. The RBCP is a singular stochastic control problem, in which both the controls and the cumulative cost process are locally of bounded variation.

math.PR↗

arXiv2005

Warm-Hot Gas in and around the Milky Way: Detection and Implications of OVII Absorption toward LMC X-3

X-ray absorption lines of highly-ionized species such as OVII at about zero redshift have been firmly detected in the spectra of several active galactic nuclei. However, the location of the absorbing gas remains a subject of debate. To separate the Galactic and extragalactic contributions to the absorption, we have obtained Chandra LETG-HRC and FUSE observations of the black hole X-ray binary LMC X--3. A joint analysis of the detected OVII and Ne IX Kalpha lines, together with the non-detection of the OVII Kbeta and OVIII Kalpha lines, gives the measurements of the temperature, velocity dispersion, and hot oxygen column density. The X-ray data also allow us to place a 95% confidence lower limit to the Ne/O ratio as 0.14. The OVII line centroid and its relative shift from the Galactic OI Kalpha absorption line, detected in the same observations, are inconsistent with the systemic velocity of LMC X--3 ($+310 {\rm km s^{-1}}$). The far-UV spectrum shows OVI absorption at Galactic velocities, but no OVI absorption is detected at the LMC velocity at $> 3σ$ significance. Both the nonthermal broadening and the decreasing scale height with the increasing ionization state further suggest an origin of the highly-ionized gas in a supernova-driven galactic fountain. In addition, we estimate the warm and hot electron column densities from our detected OVII Kalpha line in the LMC X--3 X-ray spectra and from the dispersion measure of a pulsar in the LMC vicinity. We then infer the O/H ratio of the gas to be $\gtrsim 8 \times 10^{-5}$, consistent with the chemically-enriched galactic fountain scenario. We conclude that the Galactic hot interstellar medium should in general substantially contribute to zero-redshift X-ray absorption lines in extragalactic sources.

astro-ph↗

arXiv2004

Fluid model for a network operating under a fair bandwidth-sharing policy

We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document transfers. We study critical fluid models obtained as formal limits under law of large numbers scalings when the average load on at least one resource is equal to its capacity. We establish convergence to equilibria for fluid models and identify the invariant manifold. The form of the invariant manifold gives insight into the phenomenon of entrainment whereby congestion at some resources may prevent other resources from working at their full capacity.

math.PR↗

arXiv1999

Four nearby L dwarfs

We present spectroscopic, photometric and astrometric observations of four bright L dwarfs identified in the course of the 2MASS near-infrared survey. Our spectroscopic data extend to wavelengths shortward of 5000Åin the L0 dwarf 2MASSJ0746+2000 and the L4 dwarf 2MASSJ0036+1840, allowing the identification of absorption bands due to MgH and CaOH. The atomic resonance lines Ca I 4227Åand Na I 5890/5896Åare extremely strong, with the latter having an equivalent width of 240Åin the L4 dwarf. By spectral type L5, the D lines extend over $\sim1000$Åand absorb a substantial fraction of the flux emitted in the V band, with a corresponding effect on the (V-I) broadband colour. The KI resonance doublet at 7665/7699Åincreases in equivalent width from spectral type M3 to M7, but decreases in strength from M7 to L0 before broadening substantially at later types. These variations are likely driven by dust formation in these cool atmospheres.

astro-ph↗