67 research outputs found
Combinatorics of Classical Unitary Invariant Ensembles and Integrable Systems
No full textThe first part of this thesis is devoted to the combinatorics, geometry, and effective computation of correlators of unitary invariant ensembles of random hermitian matrices with classical potentials. The main results are the subject of the publications [7, 8] with my supervisors T.~Grava and G.~Ruzza, and are summarized as follows.
We provide generating functions for correlators of general Hermitian matrix models; formulae of this sort have already appeared in the literature [1, 5], we rederive them here with different methods which lend themselves to further generalizations. Such formulae are not recursive in the genus and hence particularly effective. Moreover, these formulae express the correlators of classical unitary ensembles as linear combinations of products of discrete hypergeometric polynomials; this generalizes relations to discrete orthogonal polynomials for the one-point correlators \langle \tr M^k \rangle of the classical ensembles recently discovered by Cunden et al. [3].
Hence, we turn our attention on the combinatorial interpretation of correlators for the Laguerre and Jacobi ensembles. We prove that the coefficients in the topological expansion of Jacobi correlators are multiparametric single Hurwitz numbers involving combinations of triple monotone Hurwitz numbers. Via a simple limit, this reproduces formulae of [2] on the Laguerre ensemble. This completes the combinatorial interpretation of correlators of unitary ensembles with classical potential.
Combining results of Dubrovin et al. [4], and of Norbury [10] connecting integrable systems with enumerative geometry, we obtain ELSV-like formulae linking the multiparametric single Hurwitz numbers of LUE and JUE respectively to cubic Hodge integrals and -GW invariants.
In the second part of the thesis we analyse various integrable dynamical systems from a probabilistic point of view. Specifically, we study the spectrum of their random Lax Matrix equipped with the associated Gibbs Measure, in the spirit of [9, 11]. This is the content of the preprint [6], in collaboration with T.~Grava, G.~Gubbiotti and G.~Mazzuca.
We explicitly compute the density of states for the exponential Toda lattice and the Volterra lattice showing they are connected to the Laguerre -ensemble at high temperatures and the -antisymmetric Gaussian ensemble at high temperatures respectively. For generalizations of these system we derive numerically their density of states and compute their ground states.
[1] M. Bertola, B. Dubrovin, and D. Yang, Correlation functions of the KdV hierarchy and applications to intersection numbers over Mg,n, Phys. D, 327 (2016), pp. 30–57.
[2] F. D. Cunden, A. Dahlqvist, and N. O’Connell, Integer moments of complex Wishart matrices and Hurwitz numbers, Ann. Inst. Henri Poincar ́e D, 8 (2021), pp. 243–268.
[3] F. D. Cunden, F. Mezzadri, N. O’Connell, and N. Simm, Moments of random matrices and hypergeometric orthogonal polynomials, Comm. Math. Phys, 369 (2019), pp. 1091–1145.
[4] B. Dubrovin, S. Q. Liu, D. Yang, and Y. Zhang, Hodge-GUE correspondence and the discrete KdV equation, Comm. Math. Phys, 379 (2020), pp. 461–490.
[5] B. Eynard, T. Kimura, and S. Ribault, Random matrices, arXiv preprint arXiv:1510.04430, (2015).
[6] M. Gisonni, T. Grava, G. Gubbiotti, and G. Mazzuca, Discrete integrable systems and random Lax matrices, arXiv preprint arXiv:2206.15371, (2022).
[7] M. Gisonni, T. Grava, and G. Ruzza, Laguerre ensemble: Correlators, Hurwitz numbers and Hodge integrals, Ann. Henri Poincar ́e, 21 (2020), pp. 3285–3339.
[8] M. Gisonni, T. Grava, and G. Ruzza, Jacobi ensemble, Hurwitz numbers and Wilson polynomials, Lett. Math. Phys., 111 (2021), pp. 1–38.
[9] T. Grava and G. Mazzuca, Generalized gibbs ensemble of the Ablowitz-Ladik lattice, Circular β-ensemble and double confluent Heun equation, arXiv preprint: 2107.02303, (2021).
[10] P. Norbury, Gromov-Witten invariants of P1 coupled to a KdV tau function, Adv. Math., 399 (2022), p. 108227.
[11] H. Spohn, Generalized Gibbs ensembles of the classical Toda chain, J. Stat. Phys., 180 (2020), pp. 4–2
BOOK REVIEW: Hydraulic structures, by P. Novak, A.I.B. Moffat, C. Nalluri and R. Narayanan
No full textRecensione sul libro: "Hydraulic Modelling – an Introduction: Principles, methods and applications", di Autori: P. Novak, V. Guinot, A. Jeffrey, e D.E. Reeve
No full textSmartphone and video games overuse effects on hand joints: time for screening interventions?
No full textsj-doc-1-jvu-10.1177_15443167211033599 – Supplemental material for Microvascular Flow Imaging in a case of Portal Vein Thrombosis
No full textSupplemental material, sj-doc-1-jvu-10.1177_15443167211033599 for Microvascular Flow Imaging in a case of Portal Vein Thrombosis by Marika Santarsiere, Mariateresa Rumolo, Emilia Vergara, Arturo Brunetti and Pietro Gisonni in Journal for Vascular Ultrasound</p
Detection of pericardial effusion during Tc-99m MIBI parathyroid imaging in a patient with chronic renal failure
No full textDetection of pericardial effusion during Tc-99m MIBI parathyroid imaging in a patient with chronic renal failure
No full textCitosteatonecrosi nel neonato: un caso clinico con valutazione ecografia Dermatologia Clinica,
No full textAdenosine Coronary Vasodilation in Coronary Artery Disease: Technetium-99m Tetrofosmin Myocardial Tomography Versus Echocardiography
No full textAbstract
This study compared the results of adenosine 99mTc-tetrofosmin cardiac tomography with those of adenosine echocardiography in identifying patients with coronary artery disease (CAD) and in localizing individual stenosed, coronary vessels.
METHODS:
Twenty-six consecutive patients with suspected or known CAD had simultaneous adenosine (140 micrograms/Kg/min intravenously) 99mTc-tetrofosmin tomography and two-dimensional echocardiography. All patients had coronary angiography within 4 wk from imaging studies. Regional 99mTc-tetrofosmin activity was quantitatively measured in 78 coronary vascular territories and echocardiographic left ventricular function was assessed in corresponding regions.
RESULTS:
At coronary angiography one patient had normal coronary vessels, 12 patients one-vessel and 13 had multivessel disease (> or = 50% luminal stenosis). Among the 25 patients with CAD, 22 showed perfusion defects at adenosine 99mTc-tetrofosmin tomography (sensitivity 88%) and 17 had abnormal echocardiographic study (sensitivity 68%, p < 0.05 versus 99mTc-tetrofosmin). Agreement for the identification of patients with CAD between adenosine 99mTc-tetrofosmin tomography and echocardiography was observed in 21 (81%) of the total 26 patients, with a kappa value of 0.45. Overall sensitivity, specificity and diagnostic accuracy for detection of individual stenosed vessels were 79%, 88% and 83% for 99mTc tetrofosmin and 57%, 68% and 61% (all p < 0.05 versus 99mTc-tetrofosmin) for echocardiography. Concordance between adenosine 99mTc-tetrofosmin tomography and echocardiography in the detection of individual stenosed coronary vessels was observed in 57 (73%) of the 78 vascular territories, with a kappa value of 0.36.
CONCLUSION:
Adenosine-induced coronary vasodilation associated with quantitative 99mTc-tetrofosmin tomography is more accurate than adenosine echocardiography in identifying patients with CAD and in detecting individual stenosed coronary vessels
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