F. Thomas Bruss - Publications



Articles in Scientific Journals



1. Bruss F.T. : Branching Processes with Random Absorbing Processes

       Journal of Applied Probability, Vol. 15, pp 54-64,



2. Bruss F.T. : How to Apply a Medicament, if its Direct Efficiency is Unknown.

       Annales de la SociŽtŽ Scientifique de Bruxelles, Vol. 93, Ser. I, pp 39-54,



3. Bruss F.T. : A Counterpart of the Borel-Cantelli Lemma.

       Journal of Applied Probability, Vol. 17, pp 1094-1101,



4. Bruss F.T. : A Probabilistic Approach to an Approximation Problem.

       Annales de la SociŽtŽ Scientifique de Bruxelles, Vol. 96, Ser. I, pp 91-97,



5. Bruss F.T. : Patterns of Relative Maxima in Random Permutations.

       Annales de la SociŽtŽ Scientifique de Bruxelles, Vol. 98, Ser. I, pp 19-28,



6. Bruss F.T. : A Unified Approach to a Class of Best Choice Problems with an Unknown Number of  Options.

       Annals of Probability, Vol. 12,  pp 882-889,



7. Bruss F.T. :

       A Note on Extinction Criteria for Bisexual Galton-Watson Processes.

       Journal of Applied Probability, Vol. 12, pp 915-919,



8. Bruss  F.T.,  H.  Mahiat  et   M. Pierard:

       Sur une fonction gŽnŽratrice du nombre de records d'une suite de variables alŽatoires de longueur alŽatoire.

       Annales de la SociŽtŽ Scientifique de Bruxelles,, Vol. 100, 4, pp 139-149,



9. Bruss  F.T. : Advances in Best Choice Modelling.

       Operations Research, DGOR, 1986, Springer Verlag, pp 639-647,



10. Bruss  F.T. and S.M.Samuels :

        A Unified Approach to a Class of Optimal Selection  Problems with an Unknown Number of Options.

       Annals of Probability, Vol. 15, pp 824-830,



11. Bruss  F.T. :

       On an Optimal Selection Problem of Cowan and Zabczyk.

       Journal of Applied Probability, Vol. 24, pp 918-928,



12. Bruss  F.T. :

        Invariant Record Processes and Applications to Best Choice  Modelling. Stochastic Processes and Their Applications,

       Vol. 30, No. 2, pp. 303-316,



13. Bruss  F.T. and J.B. Robertson :  A Survey of the Linear Search Problem.

       The Mathematical Scientist, Vol. 13, No. 2, pp 75-89,



14. Bruss  F.T.

        Une note sur des inŽgalitŽs pour l'espŽrance de variables alŽatoires majorŽes ou  minorŽes.

       Annales de la SociŽtŽ Scientifique de Bruxelles,, Vol. 104,  No 1,  pp 3-8,



15. Bruss  F.T., S.R. Jammalamadaka and X. Zhou :

       On an Interval Splitting Problem.

       Statistics and Probability Letters , Vol.  10,   pp  321-324,     



16. Bruss  F.T. and S.M  Samuels:

       Conditions for Quasi-Stationarity of the Bayes Rule in Selection Problems with an Unknown Number of Options.

       Annals of Probability , Vol. 18, No. 2, pp  877 - 886,



17. Bruss  F.T. and  C.A. O'Cinneide :

       On the Maximum and Its Uniqueness for Geometric Random  Samples.

       Journal of Applied Probability, Vol. 27,  no. 3,  pp  598 - 610,




18. Bruss  F.T. and  L.C.G. Rogers :

       Pascal Processes and Their Characterization.

       Stochastic Processes and Their Applications, 

       Vol . 37,  no. 2,  pp  331 - 338,



19. Bruss  F.T. and  J.B. Robertson :

        "Wald's Lemma" for Sums of Order Statistics of i.i.d. Random Variables.

       Advances Applied Probability ,  Vol. 23,  no. 3,  pp  612 - 623,



20. Bruss  F.T. and L.C.G. Rogers :

       Embedding Optimal Selection Problems in a Poisson Process.

       Stochastic Processes and Their Applications,  Vol. 38,  pp  267 - 278,  



21. Bruss  F.T.:

       Optimal Selection, Learning, and Machine Implementation.

       Contemporary Mathematics (American Mathematical Society), Vol. 125,   pp  3 - 35.



22. Bruss  F.T. and Ferguson T.S.: Minimizing the Expected Rank with Full-Information.

         Journal of Applied Probability , Vol. 30, No 3, pp  616-626.



23. Bruss  F.T.:

Minimax Solutions for the Best Choice Problem with Random Freeze Times and  a Random Number of Options.

Volume in honour of Simone Huyberechts,

Cahiers de CERO, Vol. 36, 57-64,



24. Bruss  F.T. :

         Mathematiques et Hasard


         Volume spŽcial de la Fondation Lucia  Brouckre

         Edition FacultŽ des Sciences, pp 9-13.



25. Bruss  F.T.

         The  Fallacy of the Two Envelopes Problem.

         The Mathematical Scientist, Vol. 21, no. 2, pp 112-119,

         (1996 )



26. Bruss  F.T. and T.S. Ferguson: 

Half-Prophets and Robbins' Problem of  Minimizing  the Expected Rank with Full Information.

         Springer Lecture Notes  in Statistics, Vol. 114  Bd  I, pp 1-17,



27. Bruss  F.T. and T.S. Ferguson: 

Multiple Buying or Selling with Vector Offers.

         Journal of Applied Probability, Vol.34, no. 4, pp 959-973



28. Bruss  F.T.

On the Fallacy of the Two-Envelopes-Problem

         The Mathematical Scientist, Vol. 23., No. 1, 60-62. 



29. Bruss  F.T.

Quick Solutions for Optimal Choice Problems in Real Time .

         Stochastic Models, Vol. 14,  pp  241-264.



30. Bruss  F.T. Unerwartete Strategien



Heft 3/98, 6-9

(1998) .


b) DIE ZEIT,  (1999)


31. Bruss  F.T and G. Louchard  

Sharp Bounds for Winning Probabilities in the Competitive Rank Selection Problem

Journal of Applied Probability,  Letter to the Editor, Vol 35, No 4 , 1007-1011.




32. Bruss  F.T., Drmota M. and  G.Louchard 

The Complete Solution of the  Competitive Rank Selection Problem

         Algorithmica, Vol. 22, No.4, 413-447.



33. Bruss  F.T. and Bojkova M.

On  Waiting Times to Populate an  Environment and Questions of Statistical Inference .

         Journal of  Applied Probability, Vol. 36, No. 1,  261-267.



 34. Bruss  F.T.

Eine Strategie fuer Anspruchsvolle.

         DIE WELT,   6 May  2000

         Wissenschaft, p. 33 ff



35. Bruss  F.T.

Der Ungewissheit ein Schnippchen schlagen



          Year 2000, Volume 6,  pp 106-107.



36. Bruss  F.T. and  Rueschendorf  L.

The Switching Problem and Conditionally Specified Distributions      

The Mathematical Scientist, Vol. 25, 46-53.



37.Bruss  F.T. and  D. Paindaveine. Selecting a Sequence of  Last Successes in  Independent Trials.

         Journal of Applied Probability, Vol 37,  389-399



38. Bruss  F.T. Sum the Odds to One and Stop.

         Annals of Probability,  Vol. 28, No 3,  1384-1391.        



39. Bruss F.T. und L. Rueschendorf:  Wie schnell verfliegt die Zeit?


         (German Edition of SCIENTIFIC AMERICAN)

         Year 2001, Volume 5,  pp 110-112.



40. Bruss F.T.:  MathematischeStrategien fuer  den Alltagsgebrauch

         DIE WELT, 17 May  2001, p 35.



41. Bruss F.T. and  F. Delbaen.

 Optimal Rules for the Sequential Selection of Monotone  Subsequences of Maximum Expected Length.

         Stochastic Processes and Their Applications

         Vol 96 (200),  pp 313-342.



42. Bruss F.T. and T. S. Ferguson

High Risk and Competitive Investment Problems.

         Annals of Applied Probability.

Vol. 12, No 4, 1202-1226.



43. Bruss F.T. , Louchard. G. and Turner J.M.

     On the N-tower problem

Advances in  Applied Probability

Vol. 35, No 1,  278-294,


pdf/ps Version On the N-tower problem.



44.  Bruss F.T. and   Louchard G.

Optimal Stopping on Patterns in Strings Generated by Random Sources

Journal of Applied Probability,

Vol. 40, No 1, 49-72.


pdf/ps Version Optimal Stopping on Patterns É



45. Bruss, F. T.  A Note on Bounds for the Odds-Theorem of Optimal Stopping.

Annals of Probability, Vol 31, No 4, 1859-1861




46.  Bruss, F.T.

a)    Playing a trick on uncertainty.


Issue 50, pages 5 and 7-8.



b) Chinese title 

Translation  of 46 a) into Chinese  

by  Prof. S. R.Yang, Taiwan National University


Volume 7, pp. 564-567.



c) Japanese title

Translation of  46 a)  into Japanese

Translated by Prof. Makoto Maejima,

Keio University, Tokyo


Volume 11, pp. 60-63.



d) Como jugarsela a la incertidumbre

Translated into Spanish, by Prof. Adolfo Quir—s

 Departamento de Matem‡ticas,  Universidad Aut—noma de Madrid

 SUMA, Vol. 47, pp. 7-10.



e) Jouer un tour a lÕincertitude.

Translation of 46 a) into French

by Prof. Kirone Mallick, UniversitŽ Paris X

GAZETTE DES MATHEMATICIENS,  No 105, juillet 2005, pp. 65-68.



f) Jak przechytrzy e niepewnosci

Guest author Article  (in Polish ; translation by

by Prof. K. Szajowski, University of Wroclaw,

with comments by Marci Malawski.

DECYZJE, Nr. 4,  pp 61-70.




47. Bruss, F.T. and R. Gruebel 

New Results on the Problem of a Unique Maximum in Random Samples of  I.I.D. Random Variables,

          Annals of Applied Probability

Vol. 13, No 4,  pages 1252-1263



48.   Swan, Y and  Bruss, F.T.         

The Schwarz-Christoffel Transformation as a Tool in Applied Probability

The Mathematical Scientist

Volume 29, pp 21-32



49. Bruss  F.T.

         Strategien der besten Wahl.  


         May 2004, pp. 102-104.



50.  Bruss F.T. and F. Delbaen.

A Central Limit Theorem for the Optimal   Selection Process for  Monotone Subsequences of  Maximum Expected  Length.

Stochastic Processes and Their Applications.

Vo. 144, pp 287-311



51. Bruss, F.T.

What is known about RobbinsÕ Problem?

Journal of Applied Probability. Vol. 42, no. 1, pp. 108-120.



52.  Bruss, F.T.

         Die Mathematik politisch-strategischen Denkens

         DIE WELT.

         20-12-2005, Wissenschaft  2/3



53. Bruss, F.T.


(a)  Die Kunst der richtigen Entscheidung



June Volume 2005, Editorial  p. 3, article pp. 78-84.



(b) Le bon choix RaisonnŽ

French version based on (a)


September Volume 2005, Editorial p. 1, article pp. 56-61.



( c ) Translation of (b) into Arabic

by Prof. Boubaker-Khaled SADALLAH

 Foundation for Advancement of Science


November Vol. 11, 2005, p 3, p 8,  article pp. 74-80.



(d) The Art of a Right Decision :  Why Decision Makers

 May Want to Know the Odds-Algorithm.

English version of (a), Feature article + addendum


Issue 62, pp 15-20,



54.  Y. Swan and Bruss, F.T.

         A Matrix-Analytic Approach to the n-Player ruin problem.

Journal of Applied Probability, Vol. 43, No 3, pp 755-766.



55. Bruss, F.T.

Der Wyatt-Earp Effekt oder die betoerende Macht kleiner Wahrscheinlichkeiten


MarchVolume 2007



 56. Bruss, F.T.

         Le pouvoir inconnu dÕun modle mathŽmatique


Vol. August, 2007, pp 86-90.



57. Bruss F.T.


(Series of articles in DIE WELT at the occasion of

Jahr der Mathematik 2008  (Year of Mathematics-2008-Germany)


57-1   Eine Prognose, DIE WELT, 4 Feb. 2008

57-2   Stategische Koaltionen  , DIE WELT, 11 Feb. 2008

57-3   Mathematik  fuer Wahlkaempfer , DIE WELT, 18 Feb. 2008

57-4   Intuition und Wahrheit , DIE WELT, 25 Feb. 2008


58. Bruss F.T. and Y. Swan
        The Poisson-embedded version of Robbins problem of minimizing the expected rank.
        Journal of Applied Probability, Vol. 46, No. 1., 1-18.

59. Bruss F.T. and G. Louchard:

        The Odds-algorithm Based on Sequential Updating and its Performance.

        Advances in Applied Probability, Vol. 41, No.1, 131-154.

60. Bruss, F.T, Louchard, G. and Ward, M.:

        Inverse Auctions: Injecting unique minima into random sets.
        ACM Transactions on Algorithms, Vol. 6, Issue 1, 21. , pp 1-19.

61. Heyvaert, M. et Bruss F.T:

        La mŽthode probabiliste.
        Gazette des MathŽmaticiens, Vol. 124, pp 15-29.

62. Bruss F.T.:
        On a Class of Optimal Stopping Problems under Mixed Contraints. 

        Discrete Mathematics and Theoretical Computer Scienceclass="MsoNormal">, Vol. 12:2, pp 363-380.

63. Bruss F.T. and RŸschendorf L.:

        On the Perception of Time.
        Special invited paper,
Gerontology, Vol. 56, pp 361-370.

64. Bruss F.T.:
        Mathematicians Self-assertion and Responsibility.

        Newsletter of the European Mathematical Society
, Issue 79, pp 24-27,

65. Bruss F.T. :
        Image, Influence and Importance of Mathematics as Directives for Public Awareness.  In book Raising Public Awareness         of Mathematics.
        Springer Verlag
, Heidelberg, New York, Dordrecht, London, Part IV, pp 297-313.

66. Bruss F.T. and M. Yor :
      Stochastic Processes with Proportional Increments and the Last-Arrival Problem.
      Stochastic Processes and Their Applications

67. Bruss F.T. :

      SociŽtŽ humaine et survie - un modle de processus de ramification.

      Bulletin de la Classe des Sciences

68. Bruss, F.T, Louchard, G.
        κ best out of n rankable objects.
        Submitted for publication

69. Bruss F.T. and Yor M.:
        Last-hitting times and WilliamÕs decomposition of the Bessel-process of dimension 3.
        Submitted for publication

70. Bruss F.T. and M. Duerinckx:
        Resource Dependent Branching Processes and the Envelope of Societies.
        To appear in
Annals of Applied Probability
        Available online in Ófuture papersÓ of IMS, AnnAP

71. Bruss F.T.:
        250 years of ÓAn essay towards solving a problem in the doctrine of chances (by the late Rev. Mr. Bayes)Ó
        Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 115, Band 3, 129-133,

72. Bruss F.T.: Grenzen einer jeden Gesellschaft (with English summary).
        Jahresbericht der Deutschen Mathematiker-Vereinigung
, Vol. 116, Band 3, 137-152





Other refereed articles



O-1 Bruss, F.T.

Quelques rŽflexions sur la question "La guerre - un paradoxe?"

Comptes-rendus Inter-University Center of Post-Graduate Studies, Dubrovnik,

January Issue 1981, pp 1-7. (1981)

O-2 Bruss, F.T.

On BenfordÕs Law




O-3 Bruss, F.T.

Homage to the Abel Prize Ð Homage to Norway

          June 2005, Issue 56, pp 9-12


O-4. Bruss, F.T.
        Mathematics and Communication.
Interview by C. BartholmŽ.
        Newsletter of the Belgian Statistical Society
, Vol. 47, pp 9-12.

O-4 Bruss, F.T.

Jouer un tour ˆ lÕincertitude.

Adaptation of article 46  e) for a different readership


September Volume 2005, pp 15-18,


O-5. Bruss, F. T.

Abel in Holland and Reflections on the Abel Prize.

Newsletter of the European Mathematical Society, Issue 80, pp 20-21,


O-6. Bruss, F. T. and Kunze C.

Will climate change global security? Directing Naturwissenschaftliches Panel with Prof. Bjorn Stevens and Prof. V.         Liebig)  Tšnissteiner Kreis JahresgesprŠche, Berlin, Band 2011, pp 3-9,


O-7. Bruss, F.T. Die Schuldenkrise.

Submitted for publication.

0-8 Bruss, F.T. Review of Thomas Bayes "Essay towards solving a problem in the doctrine of chances"

O-8.(i) Zentralblatt fŸr Mathematik, 4 pages. (2012)
O-8.(ii) Newsletter of the Belgian Statistical Society, 57, 20-25, (2013)

O-9. Bruss F. T., La file unique - Interview du mathŽmaticien.
          LE SOIR (8-1-2014)

O-10. Bruss F.T. and Wajnberg A. Le thŽorme de Bruss-Duerinckx ou lÕenvelopment des sociŽtŽs humaines, Interview par A. Wajnberg,
            FNRS-News, June 2014 Issue, pp 20-21,


O-11. Bruss F.T.  Le survol de Bruxelles.
Submitted for publication.




NB:  Conference proceedings are not listed.






       Lecture Notes:


L-1. Bruss F.T. et  Hardy A. : ProbabilitŽs- Recueil d'exercices

       Candidature en sciences mathŽmatiques.

       Librairie des Sciences, FacultŽs Universitaires Notre-Dame de la Paix

       (1982) ; Revised edition (1986).


L-2. Bruss F.T. : Processus Stochastiques

       Licence en sciences mathŽmatiques.

       Librairie des Sciences  Notre-Dame de la Paix.



L-3. Bruss F.T.  Analyse sŽquentielle

       2-me Licence en sciences mathŽmatiques



L-4. Bruss F.T. MathŽmatiques GŽnŽrales.


Part I :   Candidature en sciences biologiques, gŽologiques, gŽographiques, et

pharmaceutiques et  premire  Žpreuve des ingŽnieurs en sciences agronomiques.

       UniversitŽ Libre de Bruxelles, FacultŽ des Sciences.

       (1993-1995; rŽvision 1996, 2nd revision 2001)


       Part II   Candidature en sciences biologiques

       UniversitŽ Libre de Bruxelles, FacultŽ des Sciences.

       (manuscrit 1995; rŽvision 1999, 2nd rŽvision 2001)


L-5. Bruss F.T. Principles of Strategic Thinking

       UniversitŽ Libre de Bruxelles, FacultŽ des Sciences.

       (1993,  revised 2003)





1.  Bruss F. T.,  Ferguson T.S. and  S.M.Samuels  (Editors)

       Strategies for Sequential Search and Selection in Real Time.

       American Mathematical Society,

       Contemporary Mathematics,

       Selected Papers

       Vol. 125, p i-vii,1-248.



2. Bruss F.T. and L. Le Cam  (Editors)

       Optimal Stopping, Games, Probability and Statistics.

       Lecture Notes of the Institue of Mathematical Statistics - Monograph series.

       Volume 35, pages i-xvi, 1-324.





          Interviews, broadcasts, and talks in 2014

7 Jan. 2014: Avantages et dŽsavantages de la file unique, Interview by Julien Bosseler, Ð 8 Jan. 2014: La file unique, LE SOIR, p. 20, ÐLe MathŽmaticien, LE SOIR, p.21.

21 Jan. 2014: Le thŽorme de Bruss-Duerinckx, CommuniquŽs de presse ULB in French, English, and Dutch, by Nathalie Gobbe, Nancy Dath and Laura Muris.

27 Jan. 2014: SociŽte et survie: Le thŽorme de Bruss-Duerinckx,
Radio Campus, Interview live (50 min.) of Bruss by Alexandre Wajnberg, ( Podcast: http://public.radiocampus.be/140128 Bruss Probabilite.mp3)

27 Jan. 2014: Interview of Bruss (telephone, 30 min) by Violaine Jadoule, LE SOIR.

28 Jan. 2014: Communisme ou capitalisme extröemes: aucun des deux systmes nÕest viable. Article by Violaine Jadoule on preceding interview,
LE SOIR, la Belgique, Monsoir, p.8.

18 Feb. 2014: Le thŽorme de Bruss-Duerinckx,
Interview live of Bruss and Duerinckx (30 min.) by Yasmine Boudaka in UTOPIA, Radio1, RTBF.

6 March 2014: Euromillions,
Interview of Bruss by Alexandre Carette (10 min.), Radio BEL-RTL

7 March 2014: Comment calculer la probabilitŽ de gagner en Euromillions Blackboard-interview (25 min.) of Bruss by Simon Francois +team;
two different short summaries on Journal tŽlŽvisŽ 13h et 19h, RTL-TV. (podcasts: http://www.rtl.be/info/economie/monargent/1074246/jackpot)

10 March 2014: Calcul de la probabilit ́e de gagner en Euromillions
Interview for UREM-ULB by F. Buekenhout; photo-report by Ch. Boukaert and J. Sengier (http://dev.ulb.ac.be/urem/Thomas-Bruss-et-l-Euromillion)

11 March 2014: Gesellschaftsformen und der Satz von Bruss-Duerinckx, Round-table interview (1 hour) by Tšnissteiner Kreis BrŸssel.

12 March 2014: Modles de sociŽtŽs humaines et probabilitŽs de survie, Invited presentation (1 hour + 20 min.),
Institut des Hautes Etudes de Belgique, Bruxelles.

20 May 2014: Gesellschaft und †berleben - Ein Verzweigungsprozess-Modell Invited presentation (90 minutes),
Institut fŸr Mathematische Wirtschaftsforschung,
UniversitŠt Bielefeld, Germany.

(15 Oct. 2014: Verzweigungsprozesse und der Satz der HŸlle der Gesellschaft. Inst. fŸr Mathematische Statistik, UniversitŠt MŸnster.)

(Nov. 2014: Einladung Vortrag, Mathematisches Institut, UniversitŠt Kiel.)

(Dec/Jan. 2014/5 T ̈onissteiner Kreis, Naturwissenschaftliches Panel, Harnack-Haus Max Planck Institut, Berlin.)